Low Complexity Fair Scheduling in LTE/LTE-A Uplink Involving Multiple Traffic Classes
1 Low Complexity Fair Scheduling in LTE Uplink Involving Different Traffic Classes
Atri Mukhopadhyay, Goutam Das
Abstract — Long term evolution (LTE) has already been accepted as the de-facto 4G wireless technology. However, the bulk of the research on LTE packet scheduling is concentrated in the downlink and the uplink is comparatively less explored. In uplink, mostly channel aware scheduling with throughput maximization has been studied. Further, channel aware scheduling requires an infinitely backlogged buffer model. This makes the investigations unrealistic. Therefore, in this work, we propose an LTE uplink packet scheduling procedure with a realistic traffic source. Firstly, we advocate a joint channel and buffer aware algorithm, which seeks to maximize the actual number of bits transmitted once a user is scheduled. Thereafter, we modify our algorithm to support traffic types with delay constraints. Next, we enhance our algorithm to support multiple classes of traffic. Finally, we have introduced priority flipping to minimize bandwidth starvation of lower priority traffics in presence of higher percentage of high priority traffic. In all the proposals, we have replaced the delay constraint by minimizing the packet drop due to delay violation. This further helps in reducing the problems to a well-known assignment problem.
Index Terms — Assignment, fairness, knapsack, LTE, MAC throughput, priority flipping, uplink scheduling. —————————— (cid:1) ——————————
1 I
NTRODUCTION
OBILE communication has progressed in leaps and bounds over the past few years. The demand for high data rate from the mobile users has further fueled the advent of mobile networks. Long term evolution (LTE) by the third generation partnership project (3GPP) is one of the latest mobile technologies that provide data rates of the order to megabits per second [1]. LTE can provide seamless integration of voice, video and data. As a result, LTE and LTE-Advanced have become the most promising wireless access technologies. LTE is fundamentally different from its preceding mobile wireless access technologies. LTE uses orthogonal frequency division multiple access (OFDMA) in its down-link and single carrier frequency division multiple access (SC-FDMA) in its uplink. OFDMA and SC-FDMA im-prove data rate by providing better interference man-agement [1]. Both OFDMA and SC-FDMA divide the channel into multiple sub-carriers. However, scheduling the sub-carriers to different users such that the system utilization can be maximized is not a trivial task. Till now, downlink scheduling has been under the radar of most of the researchers while uplink scheduling is a comparative-ly less explored field. In LTE, packet scheduling is the responsibility of the evolved nodeB (eNodeB). Packet scheduling refers to the act of allocating a certain group of sub-carriers for trans-mitting packets. Sub-carrier allocation is carried out in groups of 12 sub-carriers of 15 kHz each for a duration of 1 ms. This unit of allocation is known as the physical re-source block (PRB). The time duration of 1 ms defines a transit time interval (TTI). Now, it is expected that each user experiences frequency selective fading in different PRBs. Further, different users experience different chan-nel conditions on a certain PRB due to their different spa-tial positions. The channel conditions influence the modu-lation and coding scheme (MCS) that can be used on a certain PRB without violating the bit error constraints. Hence, the eNodeB has to allocate multiple PRBs to mul-tiple users with the target of maximizing the possibility of bit transmission in each and every TTI. As already men-tioned, scheduling is done on both the downlink and the uplink. LTE Downlink allows distributed allocation of PRBs [1][2]. However, in the LTE uplink, contiguous allo-cation of PRBs is more advisable due to the restrictions imposed by SC-FDMA. The contiguous PRB allocation restriction makes the assignment problem NP-Hard [3]. Further, when real-time packets with quality of ser-vice (QoS) constraints are scheduled, the scheduler has to worry about delay deadlines and packet drop constraints. In order to get around the problem of meeting delay deadlines, proposals with a two-stage scheduling are available in the literature [4][5]. The first stage is called time-domain packet scheduling (TDPS), while the second stage of scheduling is known as the frequency domain scheduling (FDPS). The TDPS shortlists the users based on head of the line (HoL) packet delay. Thereafter, the FDPS seeks to allocate the PRBs to the shortlisted users [4] with the target of maximizing the system throughput in terms of bits transmitted. Unfortunately, considering a subset of users for the final allocation results in sub-optimal solutions [4]. In order to compute an optimal so-lution, one should investigate all possible options while keeping the computational complexity under control. Moreover, most of the algorithms (for both downlink and uplink) existing in the literature consider infinitely backlogged model for data traffic and carry out only channel aware scheduling [3][4][6][7][8][9]. These models consider that packets are always available for transmis- ———————————————— • A. Mukhopadhyay and G. Das are with G. S. Sanyal School of Telecommu-nications, Indian Institute of Technology Kharagpur, India (e-mail: [email protected]; [email protected]). M sion in the UE buffer. These algorithms, in fact, allocate the PRBs to the UEs that possess good channel gains even though the UEs may not have sufficient data in their buff-er to utilize the allocated PRBs. However, the MAC throughput, which is the actual number of bits transmit-ted, may remain low as actual buffer status is not consid-ered while scheduling the UEs [10]. Similar approach can be found in [11] where the authors have considered a buffer-based channel dependent scheduler (BCS) for two-hop relay-assisted LTE network. However, BCS is not an optimal algorithm and it does not guarantee contiguous channel allocation, which is a requirement as per LTE standards. In addition, UE has to send huge control in-formation because the UE requires sending data in differ-ent non-contiguous PRBs with different modulation schemes. In LTE scheduling, the final frontier is reached when we try to deal with traffic of multiple classes. Different classes of real-time traffic have different delay require-ments. Moreover, data traffic, which is of best-effort type, has no delay requirements. The authors of [12] proposed two algorithms that emphasizes on QoS based resource allocations in LTE uplink. The proposals facilitate the packets of the ongoing flows to remain within delay deadlines while meeting a minimum rate constraint. However, the algorithms follow a greedy approach and hence do not provide optimum allocations. Two classes of traffic with different QoS requirements have been dealt with in [13] by switching between two heuristic algo-rithms. The work in [14] proposes a delay-aware algo-rithm that follows heuristic riding the peaks method of [3]. In [15], a standard complaint scheduling scheme for LTE-Advanced is discussed. The proposal describes a three stage adaptive and potential aware scheduling scheme (APASS) that carries out the PRB allocation for the traffic in a buffer while maintaining QoS. The final stage of APASS improves the scheduling performance of the initial allocation by following a potential zone con-cept. However, the user elimination method described in the second stage of APASS is heuristic and therefore, may result in suboptimal allocation. Further, APASS has a worst case complexity of (cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:2)(cid:3), (cid:8)(cid:9) (cid:10) log (cid:14) (cid:8) + (cid:8)(cid:16)(cid:9) , where (cid:8) is the number of resource blocks, (cid:3) is the num-ber of active users and (cid:16) is the number of schedulable users. In this paper, we have developed an optimization problem for LTE uplink scheduling, which overcomes all the above difficulties with mathematical subtleties. The paper is organized as follows. Section 2 provides a motivation to the problem. Section 3 provides the de-tails of the proposed delay aware packet scheduling algo-rithm. Section 4 sheds light on the delay and fairness aware traffic scheduling paradigm for mixed traffic. Sec-tion 5 provides a discussion on the algorithmic complexi-ties of the proposals. Section 6 discusses the simulation model. Section 7 showcases the results and discussion followed by the conclusion.
2 M
OTIVATION
In this section, we discuss the issues related to chan- nel aware scheduling that provide us the motivation to include buffer status within the same framework. There-after, we introduce real-time traffic streams scheduling and demonstrate that even channel plus buffer aware scheduling is not enough when traffic with delay dead-lines are considered. We provide an example with three UEs that are competing for a single resource chunk (RC) to highlight the motivation for our proposed method. An RC is comprised of a set of six contiguous PRBs. In this example, we assume that the channel quality indicator (CQI) value does not change through the length of our example of five TTIs. In this example, we also assume that the number of bytes arriving per TTI to each of the users is deterministic and has a fixed value of 50. These as-sumptions are for the sake of maintaining simplicity. Lat-er on, we prove through simulation that the conclusions drawn over here are rather generic. Table 1 provides the relationship between a certain CQI index value and the number of bytes of data that can be transmitted with the supported type of modulation. Table 2, on the other hand, illustrates the initial conditions. As mentioned before, only channel aware scheduling, while neglecting the buffer conditions is not optimal and it induces unfairness. The UEs closer to the eNodeB are scheduled more frequently as they generally possess bet-ter channel gains. However, the UEs with poorer channel gains do not get enough transmission opportunities, which results in higher delay and packet loss [10]. T ABLE M APPING OF
CQI
TO DATA TRANSMISSION WITHIN A
TTI
CQI Index Modulation Data (1 PRB) Data (1 RC=6PRBs) 1-6 QPSK 42 252 7-9 16-QAM 84 504 10-15 64-QAM 126 756 T ABLE E XAMPLE
CQI
AND B UFFER
UE CQI (C) Data transmission possible (bytes) (P) Arrival rate (bytes/second) Initial buffer size (bytes) (B) 1 7 504 50 400 2 12 756 50 300 3 6 252 50 260
On the other hand, if buffer aware scheduling is used (see Table 3), the scheduling parameter becomes the min-imum of the number of bytes that the channel condition allows to transmit for a particular UE and the number of bytes present in that UE’s buffer. This clearly increases fairness as the buffer occupancy also becomes a deciding factor. As a result, different users are selected in different TTIs (marked in bold). Hence, the overall system MAC throughput improves. We present a few examples in the following tables to support our argument. The bold fonts in Table 3-5 indi-cate the scheduled users. The values in TTI(i+1) column of Table 3-5 indicate the updated values from TTI(i) col-umn after accounting for the arriving and transmitted bytes. For example in Table 3, TTI(2) column value for UE1 is calculated by subtracting the number of bytes transmitted during TTI(1) (400) from the buffer content at the beginning of TTI(1) (400) followed by an addition of the number of newly arriving bytes (50). In Table 4 and Table 5, we deal with traffic having delay deadlines. The number on the left side of the “/” indicates the buffer content and the number on the right side presents the number of bytes to be dropped if they are not transmitted in the current TTI. In this example, we assume that 20 bytes cross delay deadline in every TTI. Channel plus buffer aware scheduling is not very effec-tive in this regard as can be seen in Table 4. The real-time packets have delay limits after which the packets are dropped. This may lead to a situation where the disad-vantaged user suffers from heavy packet drop due to de-lay violation. Thus, the buffer content of these needy us-ers may remain low and the scheduler may not allocate them bandwidth for data transmission. As a result, the system throughput over long term degrades and packet loss increases. T ABLE C HANNEL PLUS B UFFER A WARE S CHEDULING
UE Buffer (bytes) TTI(1) TTI(2) TTI(3) TTI(4) TTI(5) 1
50 100 150
2 300
50 100 150 3 260 310
360 158 Therefore, to overcome this, packet delay can be a pa-rameter to be further considered in such a scenario. How-ever, minimizing delay (measured in seconds) and max-imizing transmitted data (measured in bytes) makes the problem multi-dimensional. Further, putting a hard con-straint on delay may lead to infeasibility when the num-ber of delay constraint violating users is larger than the number of available resource units. This may result in non-functional scheduler. Hence, one needs to choose a parameter carefully to take care of both the problems mentioned above. We observe that the number of packets dropped if a user is not scheduled provides an elegant solution. Thus, we propose to maximize system through-put while simultaneously minimizing the overall packet drop. Since both the parameters are measured in bytes, a single objective function can be framed by subtracting the number of bytes that will be dropped after scheduling from the number of bytes that will be transmitted. Similar approach is taken in case of mixed traffic. In this case, the “packets to be dropped” metric captures the packets that will be dropped from each of the constituting traffic clas-ses if the UE is not scheduled. In our example, we can clearly see that in the first TTI, UE3 should be scheduled as it faces the danger of heavy packet drop. However, if only channel plus buffer aware scheduling is used, UE1 is selected (see Table 4). On the other hand, if we schedule UE3 based on our new objective (see Table 5), then heavy packet drop can be avoided at the expense of lower MAC throughput. We see that if UE1 is selected, then the objective value becomes (cid:2)400 − 100 − 255 = 45(cid:9) . On the other hand, scheduling UE2 yields (cid:2)300 − 50 − 255 = −5(cid:9) . Finally, scheduling UE3 results in (cid:2)252 − 50 − 100 = 102(cid:9) . Hence, the pro- posed scheduler schedules UE3. This procedure continues in every TTI. From this example, we can observe that our proposal improves the final MAC throughput and reduc-es the overall packet drop as well. Overall, this entails a requirement for cross layer op-timization while scheduling. However, taking both the traffic and channel gain matrix into the consideration for scheduling, the eNodeBs require a high complexity algo-rithm. Further, including QoS into the optimization func-tion requires further adjustment in algorithm designing in order to keep the algorithmic complexity checked within the polynomial time. T ABLE C HANNEL PLUS B UFFER A WARE S CHEDULING FOR REAL TIME TRAFFIC
UE Buffer/Packets to be dropped (bytes) TTI(1) TTI(2) TTI(3) TTI(4) TTI(5) 1
2 300/100
3 260/255 55/5 100/20
400 250 100 130 130 1010 Total Drop 355 5 20 20 20 420 T ABLE C HANNEL PLUS B UFFER A WARE S CHEDULING FOR REAL TIME TRAFFIC CONSIDERING PACKET DROP
UE Buffer;Packets to be dropped (bytes) TTI(1) TTI(2) TTI(3) TTI(4) TTI(5) 1 400/50
2 300/100 250/20
Finally, to deal with multiple classes of real time traf-fic, the UE must judiciously use the allocated bandwidth. The existing schedulers in the UE employ strict priority scheduling where the voice queue is emptied first, fol-lowed by the video queue and the data queue respective-ly. This can lead to bandwidth starvation for the lower priority traffics, especially if the percentage of higher pri-ority traffic is high in the traffic composition. Bandwidth starvation hinders the overall service quality. Hence, if the transmission of the higher priority traffic class can be safely delayed without violating its delay constraints in a certain TTI, the traffics of lower priority classes can be selected for transmission. We call this procedure as priori-ty flipping. Priority flipping can significantly improve the user experience. The contributions of this paper can be listed as fol-lows: We propose a delay aware real time scheduling algo-rithm that considers delay constraints for a single class of traffic while maximizing the number of bits transmitted. This algorithm tries to schedule the most deprived user. 2.
Thereafter, we upgrade the algorithm for handling voice, video and data traffics that have different QoS requirements. Finally, priority flipping has been introduced in the UE side to further enhance the QoS of lower priority classes while maintaining minimum QoS require-ments of the higher priority class. D ELAY AWARE REAL - TIME TRAFFIC SCHEDULING
In this section, we explain our previously proposed Dynamic Hungarian Algorithm with modification (DHAM) [10]. Thereafter, we extend DHAM to consider delay aware real time traffic and to support QoS when only a single type of traffic is being transmitted. We list the symbols used in the following sections in Table 6. T ABLE S YMBOLS
Symbols Description N U Number of active UEs. M Number of RCs. Ω Set of delay violating users. N D |Ω| . CA based scheduling is an elegant solution to sched-uling problems in LTE upstream. However, one must remember that CA scheduling assumes infinitely back-logged model. Unfortunately, this assumption does not always hold in real world networks. Hence, along with CA, a buffer aware scheduling mechanism has to be in-troduced to enhance scheduling efficiency. We intro-duced such an algorithm (DHAM) in our previous work [10]. As explained in Section 2, for DHAM, one needs to prepare the channel gain matrix ( C ) and buffer status ( B ) as shown in Table 2. Thereafter, P matrix is prepared, which signifies the number of bits that can be transmitted (refer Table 2) by mapping the elements of matrix C to values found by fol-lowing the MCS given in Table 1. In our example, we have ignored the effect of coding and the corresponding P matrix values are represented in bytes. Next, the elements of traffic matrix W is prepared as follows: (cid:27) (cid:28),(cid:29) = (cid:4)(cid:30)(cid:31) ! (cid:28),(cid:29) , " (cid:28) (1) where, (cid:27) (cid:28),(cid:29) is the element of traffic matrix W that cor-responds to the i th UE and the j th RC; ! (cid:28),(cid:29) is the element of matrix P that corresponds to the i th UE and the j th RC (maximum possible number of bytes that the i th UE can send on the j th RC) and " (cid:28) is the element of the vector B that corresponds to the i th UE. In (1), the (cid:4)(cid:30)(cid:31) ! (cid:28),(cid:29) , " (cid:28) is considered because even if ! (cid:28),(cid:29) is greater than " (cid:28) , the UE will not be able to send more data than " (cid:28) ; since, after sending " (cid:28) , the UE will have no more data to send in the current TTI. On the contrary, if ! (cid:28),(cid:29) is smaller than " (cid:28) , the UE will be able to send at most ! (cid:28),(cid:29) due to physical chan-nel capacity constraints. Thus, applying equation (1) over the example of Ta-ble 2, we get the final Traffic Matrix ( W ). Utilizing the prepared W matrix, the scheduling op- eration is performed with the help of Integer Linear Pro-gram (ILP) (2-5). %(cid:5)(cid:6)(cid:30)(cid:4)(cid:30)&' ∑ ) (cid:28),(cid:29) (cid:27) (cid:28),(cid:29)(cid:28),(cid:29) (2) Subject to the constraints, ∑ ) (cid:28),(cid:29)(cid:28),(cid:29) = % (3) ∑ ) (cid:28),(cid:29)(cid:28) ≤ 1, ∀, (4) ∑ ) (cid:28),(cid:29)(cid:29) ≤ 1, ∀(cid:30) (5) where, (cid:27) (cid:28),(cid:29) - . is obtained from (1) ; ) (cid:28),(cid:29) is a binary variable, which is equal to 1 if UE (cid:30) is allocated to RC , . Otherwise, ) (cid:28),(cid:29) = 0 . The constraint (3) specifies that the number of allocations should be equal to the number of RCs present. The constraint (4) implies that an RC can be allocated to only a single UE. The constraint (5) signifies that one UE can get at most one RC. In [10], we have shown that the scheduling problem falls under the category of the well-known assignment problem and Hungarian algorithm can be applied to solve it in polynomial time. However, it is to be noted that assignment problems require equal cardinalities of both the partites. Whereas, for the above mentioned scheduling, (cid:8) is generally greater than % . Therefore, one needs to use Hungarian algorithm after adding dummy RCs to transform the optimization problem to an assign-ment problem. The costs/rewards of connecting UEs to dummy RCs are set to zero. Therefore, the UEs that get allocated to dummy RCs are considered to be the UEs with no allocation in the current TTI. CA-Hungarian [7] and DHAM maximizes PHY throughput and MAC throughput respectively. DHAM works optimally when used with best-effort traffic. How-ever, when we have traffic with delay constraints, i.e., real-time traffic, DHAM may inadvertently degrade the QoS. Examples of real-time traffic are voice and video. Since, DHAM is both CA and buffer aware, it is inclined towards scheduling the UEs with better channel quality. The users with poor channel quality may not get the op-portunity for transmission even when their buffer builts up. Moreover, for real-time traffic, if a packet is not transmitted within its deadline, the packet is dropped. This results in further deterioration of the QoS. Hence, DHAM requires further modifications to ensure that it works efficiently for real-time traffic. The resulting modi-fied protocol is termed as delay aware real-time schedul-ing (DARTS). DARTS uses the same traffic matrix (W) used for DHAM. The criterion for scheduling a user using DARTS can be summarized using the following ILP. %(cid:5)(cid:6)(cid:30)(cid:4)(cid:30)&' ∑ ) (cid:28),(cid:29) (cid:27) (cid:28),(cid:29)(cid:28),(cid:29) (6) Subject to the constraints, ∑ ) (cid:28),(cid:29)(cid:28) ≤ 1, ∀, (7) ∑ ) (cid:28),(cid:29)(cid:29) ≤ 1, ∀(cid:30) (8) (cid:28) (cid:28)(cid:29)(cid:29) − 5, ∀(cid:30) (9) In the ILP (6-9), the constraints have inequalities in order to accept unequal number of RCs and UEs. The constraint (7) means that an UE, if scheduled, can have at most one RC. Constraint (8) implies that an RC can be allocated to at most one UE. The constraint (9) is used to ensure that a real-time packet is scheduled within its de-lay constraints. Here, (cid:28) indicates the delay of the head of the line (HoL) packet of the i th UE. If the UE has been scheduled in the current TTI then (cid:28),(cid:29)(cid:29) , oth-erwise it is equal to 1. represents the delay deadline for the considered traffic and is the length of the TTI. The entire inequality enforces scheduling of an UE when its HoL packet will cross its delay deadline if not sched-uled in the current TTI. > 9 : ILP (6-9) works well as long as (cid:8) : < % . Otherwise, the ILP (6-9) becomes infeasible. A possible solution is to formulate two ILPs. When (cid:8) : < % , use ILP (6-9); otherwise shortlist only the set < (refer Table 6) and execute DHAM on them, which has no delay constraint. However, the problem of executing DHAM only on set < does not capture the number of packets that will be dropped if = - < is not scheduled in the current TTI. This is further illustrated in Table 7 with a suitable example. Here, UE 2 has relatively better channel conditions but with fewer packets facing the risk of dropping. UE 1, on the other hand, has relatively poorer channel conditions but has a large number of packets about to be dropped in its buffer. Therefore, in order to enforce fairness, we should ideally prefer the scheduling of UE 1 over UE 2. However, DHAM will do the opposite. Moreover, we also need to minimize packet drop arising from the resulting scheduling. In another example that is shown in Table 8, we can clearly see that scheduling UE1 (more critical us-er) leads to a drop of (298+500=798) bytes. On the other hand, scheduling UE2 leads to a drop of 550 bytes. This will no doubt lead to slight unfairness, but it is better from the systems’ perspective. In other words, by sched-uling UE2, we are avoiding future packet drop; thereby, controlling long term system throughput indirectly. DARTS ensures fairness over time and at the same time it enhances delay awareness without causing infeasibility. T ABLE E XAMPLE T RAFFIC : C ASE UE Data transmis-sion possible (bytes)
Bytes to be dropped
1 252 260 2 504 100 T ABLE E XAMPLE T RAFFIC : C ASE UE Data transmis-sion possible (bytes)
Bytes to be dropped
1 252 550 2 504 500
Thus, in order to ensure fairness and minimize pack-et drop we need to modify the objective function of the optimization procedure used in DHAM. So, the new ob-jective function becomes – %(cid:5)(cid:6)(cid:30)(cid:4)(cid:30)&' ∑ ∑ ) (cid:28)(cid:29) (cid:27) (cid:28)(cid:29) − > (cid:28)(cid:29) (cid:29)(cid:28) − ∑ ? (cid:28) @ (cid:28)(cid:28) (10) Subject to the constraints, ∑ ) (cid:28)(cid:29)(cid:28) = 1, ∀, (11) ∑ ) (cid:28)(cid:29)(cid:29) ≤ 1, ∀(cid:30) (12) ? (cid:28) + ∑ ) (cid:28)(cid:29)(cid:29) = 1, ∀(cid:30) (13) ) (cid:28)(cid:29) = 0 AB 1 (14) ? (cid:28) = 0 AB 1 (15) where, @ (cid:28) is the number of bytes that will be dropped if UE (cid:30) is not scheduled in the current TTI and > (cid:28)(cid:29) is the number of bytes that will be dropped by UE (cid:30) if UE (cid:30) is allocated to RC , . Constraint (13) ensures that UE (cid:30) is ei-ther allocated an RC ( ∑ ) (cid:28)(cid:29)(cid:29) = 1 ) or the UE is mapped to the dummy RC ( ? (cid:28) = 1 ). We replace (cid:27) (cid:28)(cid:29) − > (cid:28)(cid:29) by C (cid:28)(cid:29) for compact representation. The problem described by Table 7 has been taken care of by the ∑ ? (cid:28) @ (cid:28)(cid:28) term. On the other hand, consideration of ∑ ∑ ) (cid:28)(cid:29) > (cid:28)(cid:29)(cid:29)(cid:28) handles the problem described by the example in Table 8. The UE i can report the value of @ (cid:28) along with the buffer status using a long buffer status report. It is impractical for the eNodeB to evaluate @ (cid:28) as it will require the delay values of all the packets. Hence, ILP (10-15) effectively replaces the delay con-straint of ILP (6-9) by the packet drop metric. Now, look-ing closely at the objective function (10) and the constraint (13), we can identify that we can equate ) (cid:28)(cid:2)DEF(cid:9) = ? (cid:28) and treat C (cid:28)(cid:2)DEF(cid:9) = −@ (cid:28) . This modification makes the packets about to be dropped if not scheduled equivalent to a dummy RC and the dummy RC can have an inflow of (cid:2)(cid:8) − %(cid:9) . These (cid:2)(cid:8) − %(cid:9) inflows are connected to the UEs that are not scheduled. For this discussion, we as-sume that (cid:2)(cid:8) > %(cid:9) . Interestingly, ILP (10-15) becomes equivalent to the famous transportation problem (ILP (16-20)) with the divergence of the last dummy RC node be-ing equal to (cid:2)(cid:8) − %(cid:9) . So, the new formulation is given by ILP (16-20). %(cid:5)(cid:6)(cid:30)(cid:4)(cid:30)&' ∑ ∑ ) (cid:28)(cid:29) C (cid:28)(cid:29)DEF(cid:29)GF(cid:28) (16) Subject to the constraints, ∑ ) (cid:28)(cid:29)(cid:28) = 1, ∀, = 1,2, … , % (17) ∑ ) (cid:28)(cid:29)(cid:28) = (cid:8) − %, ∀, = % + 1 (18) ∑ ) (cid:28)(cid:29)(cid:29) = 1, ∀(cid:30) (19) ) (cid:28)(cid:29) = 0 AB 1 (20) Constraint (18) implies that the dummy node can have an inflow of (cid:2)(cid:8) − %(cid:9) . The other constraints are same as ILP (2-5). Finally, in order to convert ILP (16-20) to an assign-ment problem (ILP (21-24)), we have to replicate the dummy RC node to create (cid:2)(cid:8) − %(cid:9) dummy RCs and restrict the inflow of each of the dummy RCs to 1. In graphical terms, we will create as many dummy nodes as required to make the cardinalities of both the partities equal. The cost of connecting to each of the dummy nodes will be same for a certain UE. Fig. 1 is a graphical repre- sentation of the creation of the dummy RCs. We have shown the edges for only one UE for brevity. The reader should visualize that every node of the left partite is con-nected to every element of the right partite in similar manner. This formulation allows us to use the low com-plexity Hungarian algorithm to solve our problem. %(cid:5)(cid:6)(cid:30)(cid:4)(cid:30)&' ∑ ∑ ) (cid:28)(cid:29) C (cid:28)(cid:29)I J (cid:29)GF(cid:28) (21) Subject to the constraints, ∑ ) (cid:28)(cid:29)(cid:28) = 1, ∀, = 1,2, … , %, (cid:2)% + 1(cid:9), … , (cid:8) (22) ∑ ) (cid:28)(cid:29)(cid:29) = 1, ∀(cid:30) (23) ) (cid:28)(cid:29) = 0 AB 1 (24) where, constraint (22) captures the conditions of con-straints (17) and (18) of ILP (16-20). We consider (cid:8) > % where are the actual RCs and (cid:2)% + 1(cid:9), … , (cid:8) denote the dummy RCs. Finally, if (cid:8) : > % , then all the = - < can not be scheduled in the current TTI. This will inevitably lead to packet drop for the users that are not scheduled. There-fore, in order to ensure that these users get higher priority in the subsequent TTIs, the number of bytes that are dropped at the end of the current TTI will be added to the obtained @ (cid:28) for the ensuing TTI. For long term fairness enforcement, this packet drop history can be recorded for a window of the past (cid:31) TTIs and the sum can be used in the (cid:2)(cid:31) + 1(cid:9) TTI. The procedure is given in (25) @ (cid:28) = ∑ K (cid:28)L(cid:28)GF (25) where, K (cid:28) is the packet drop history for the (cid:30) TTI. (a) (b)
Figure 1. Bipartites showing UE and RCs and the costs of connecting them. (a) without adding dummy RCs. (b) adding dummy RCs with same cost for each UE (assignment problem). M < 9 : For the previous discussions in Section 3.2, we have considered that N O > M . However, another case may arise where N O < M . In such a scenario, if we allow only one RC per UE, some RCs will be wasted which could have been used by the active UEs. Therefore, we use ILP (10-15) in an iterative manner for this purpose. However, we omit the > (cid:28)(cid:29) term for this purpose. The term > (cid:28)(cid:29) is ob-tained through preprocessing by considering the fact that a certain UE will be allocated only a single RC. But, in this scenario, there is a scope for allocation of multiple RCs to a single UE. Hence, the calculation of > (cid:28)(cid:29) becomes de-pendent on the allocations arising from multiple itera-tions. As a result, including > (cid:28)(cid:29) will lead to sub-optimal allocations. Further, we prove through simulations that the effect of using > (cid:28)(cid:29) is minimal in such a scenario. Moreover, @ (cid:28) is made equal to the number of bytes that will be dropped if UE (cid:30) is not scheduled in the cur-rent TTI. We can clearly see that as long as the number of UEs is less than the number of RCs considered for alloca-tion, the term ∑ ? (cid:28) @ (cid:28)(cid:28) does not play any role in the alloca-tion. At the end of every iteration, the values of @ (cid:28) are updated by subtracting the number of bytes that will be transmitted by UE i due the allocation obtained in the current iteration. The minimum value that @ (cid:28) can attain is equal to zero. In the final iteration, the updated value of the term ∑ ? (cid:28) @ (cid:28)(cid:28) ensures that the delay violating UEs may be exclusively considered. It should be noted that since N O < M , dummy UEs with zero buffer content are added in this case for framing an assignment problem.
4 D
ELAY AND F AIRNESS AWARE TRAFFIC SCHEDULING FOR MIXED TRAFFIC
In this section, we propose a delay-aware fair sched-uling algorithm for mixed traffic (DAFS) that maximizes the MAC throughput while meeting minimum QoS con-straints when multiple traffic types are being scheduled. Thereafter, we propose priority flipping at the UE to fur-ther mitigate lower priority traffic starvation.
In Section 3, a single class traffic with delay deadline was considered. However, one must look into multiple classes of traffic because a single user may generate voice, video and data packets at the same time. These different types of traffics have varying QoS requirements. For ex-ample, voice generally has stringent delay bounds (less than 50 ms) for the air interface [5]. Video, on the other hand, has to satisfy relatively relaxed delay deadlines (less than 150 ms) [5]. Finally, data has no delay con-straints. However, data packets may suffer from band-width starvation if the real time traffic load is sufficiently high. Hence, we need to take care of each of the traffic types individually in order to provide overall user satis-faction; which demands that we must feed parameters relating to each of the traffic types in the optimization engine. However, allowing too many parameters to enter into the optimization algorithm makes the convergence time impractical from the implementation point of view. Therefore, we construct a single parameter that ensures the individual delay bounds of each classes present in the considered traffic mix. This further keeps the execution time of the optimization algorithm within practical limits. Our modified metric ( @ (cid:28) ) for i th user is given below, @ (cid:28) = (cid:4) (cid:28)QR + (cid:4) (cid:28)Q(cid:28) + (cid:4) (cid:28)S (26) where, (cid:4) (cid:28)QR = the number of voice packets that will be dropped, if the user is not scheduled in the current TTI; (cid:4) (cid:28)Q(cid:28) = the number of video packets that will be dropped if the user is not scheduled in the current TTI; and (cid:4) (cid:28)S = the number of bytes in the buffer that is above a pre-defined buffering threshold (cid:2)T U4 in bytes(cid:9) . RC1RC2RC3UE1UE2UE3UE4 γ γ γ UE5
RC1RC2RC3Dummy RC4UE1UE2UE3UE4 γ γ γ -k UE5 Dummy RC5 -k This @ (cid:28) value is further used for the proposed algo-rithm for single class ILP (21-24). This ensures that a UE with urgent requirements is always preferred for schedul-ing. Following the model used in DARTS, the UE will report the value of @ (cid:28) along with the buffer status to the eNodeB. In this sub-section, we mitigate lower priority traffic starvation. In contrast to the algorithms discussed so far, where the primary processing is done in the eNodeBs and UEs employ a strict priority packet forwarding, DAFS with priority flipping (DAFS-PF) employs additional op-timization at the UE. In strict priority transmissions, the order of priority followed is voice, video and then data. However, in strict priority transmission, if the higher priority traffic compo-sition is sufficiently high then there is constant arrival of traffic in the higher priority buffers. This results in defer-ring of the lower priority packet transmission as the lower priority packets are transmitted only when all the higher priority traffic buffers are empty. Hence, the lower priori-ty packets may suffer from starvation. Therefore, in DAFS-PF, the UE may increase the pri-ority value of the lower priority packets if it senses the development of a possible starvation. In order to achieve this, we associate rewards to packets and our target is to maximize the rewards while filling up the allocated bandwidth such that it is not over flowed. This require-ment matches with the requirements of a knapsack prob-lem. The problem is formally defined as follows. %(cid:5)(cid:6)(cid:30)(cid:4)(cid:30)&' ∑ ∑ ) (cid:28)(cid:29) B (cid:28)(cid:29)(cid:29)(cid:28) (27) Subject to the constraints, ∑ ∑ ) (cid:28)(cid:29) (cid:27) (cid:28)(cid:29)(cid:29)(cid:28) ≤ ` (28) ) (cid:28)(cid:29) = 0 AB 1 (29) where, , ∈ bcA(cid:30)d', c(cid:30)>'A, >(cid:5)5(cid:5)e , ) (cid:28),(cid:29) is a binary variable indicating the scheduling information of the i th packet of the j th type, B (cid:28),(cid:29) is the reward associated with the i th packet of the j th type, (cid:27) (cid:28),(cid:29) is the size of the i th packet of the j th type and ` is the allocated bandwidth. Next, we explain the design of the reward variables that suits our purpose. B (cid:28),QR(cid:28)lm = : n,op : qr,op , B (cid:28),Q(cid:28)SmR = : n,on : qr,on , (30) B (cid:28),Ss3s = t u vt qr (cid:2)tvt qr (cid:9) (cid:30)w T l > T U4 (31)
0 A5ℎ'B(cid:27)(cid:30)y' where, (cid:28),QR is the i th voice packet delay, (cid:28),Q(cid:28) is the i th video packet delay, U4,QR is the voice delay threshold, U4,Q(cid:28) is the video delay threshold, T l is the current buffer occupancy, T U4 is the buffer threshold and T is the buffer capacity. The explanations of the reward metrics are as fol-lows: For both voice and video, as the delay of a packet approaches the maximum delay for which the packet can be stored in the buffer, the reward for transmitting the packet increases. Therefore, if video is getting starved due to high input of voice packets, at some point of time B (cid:28),Q(cid:28)SmR will be greater than B (cid:28),QR(cid:28)lm and hence the video packet will get transmitted prior to the voice packets. However, data packets are not of the class of real time traffic and therefore, cannot be associated with de-lay. Hence, we choose buffer build up as the metric for prioritizing data packets. Since, data packets can be de-layed, they are not given any priority when T l < T U4 . However, when T l > T U4 and data packets are present in the buffer, we can say that the data packets are being starved due to the presence of other higher priority pack-ets. Therefore, the data packets are marked and same amount of reward is associated to each and every marked data packet. The priority among the data packets follows first-in-first-out principle. Therefore, as the buffer gets filled up more and more, the priority of the data packets gets increased and they become more likely to be trans-mitted. Hence, DAFS-PF seeks to mitigate lower prioirty traffic starvation. In order to minimize the execution time of the algo-rithm, these metric calculations must be a part of prepro-cessing before every scheduling instance. During the scheduling instance, only the knapsack algorithm is exe-cuted. The design of the algorithm will be such that all the metrics (rewards) will be recalculated while packet transmissions in the preceding TTI are ongoing. This helps in minimizing scheduling delay. A N OTE ON C OMPLEXITY
The creation of the traffic matrix involves (cid:1)(cid:2)(cid:4)(cid:31)(cid:9), where (cid:4) is the number of RCs and (cid:31) is the number of UEs. For creating a symmetric matrix, the complexity be-comes (cid:1)(cid:2)(cid:4)(cid:5)(cid:6)(cid:2)(cid:4), (cid:31)(cid:9) (cid:14) (cid:9) . The traffic creation matrix of DARTS and DAFS is (cid:1) (cid:4)(cid:2)(cid:31) + 1(cid:9) . The assignment complexity is same as that of (cid:1)(cid:2)(cid:4)(cid:5)(cid:6)(cid:2)(cid:4), (cid:31)(cid:9) (cid:10) (cid:9) . Thus, the complexity is (cid:1)(cid:2)(cid:4)(cid:5)(cid:6)(cid:2)(cid:4), (cid:31)(cid:9) (cid:10) (cid:9) + (cid:1)(cid:2)(cid:4)(cid:5)(cid:6)(cid:2)(cid:4), (cid:31) + 1(cid:9) (cid:14) (cid:9) . The user side action of DAFS-PF has to perform a us-er procedure following the knapsack optimization para-digm. The optimization solution has been obtained through the greedy method as there is packet fragmenta-tion provision in LTE. The resulting complexity is (cid:1)(cid:2)(cid:31) log (cid:31)(cid:9) .
6 S
IMULATION M ODEL
The simulation studies have been carried out on a system level simulator developed in the OMNeT++ net-work simulator. We have considered a seven cell scenario (Fig. 2), where a single cell is surrounded by six first tier cells. The studies have been carried out on the center cell, which acts as the serving cell and the first tier cells pro-vide the interfering signal power. All the results obtained have been recorded in the center cell. The UEs have been deployed in the cells by following a Poisson point process. In this paper, we have assumed that all the UEs are directly connected to its serving eNodeB. Uplink transmission power control and MCS have been considered as per the guidelines provided in [16]. We have used a block fading channel model, where the channel conditions remain constant over a TTI [11][19]. The work assumes that the UEs are not mobile. However, the work is perfectly valid for users with mo-bility. Further, we assume that the eNodeB has knowledge of the CQIs, buffer lengths and critical packets of all the UEs at the time of taking the scheduling deci-sions. For changing the input voice load, we have varied the generation interval of the packets of a two-state Mar-kov VoIP Model [16]. Similarly, for the video model [17] we have altered the frames per second in order to vary the load. The load of the self-similar data source has been varied following the method given in [21]. The details of the simulation parameters are listed in Table 9 and Table 10 [16][19].
Figure 2. Simulation Model T ABLE T RAFFIC M ODELS
Parameter
Values
Voice traffic model two-state Markov [16] Voice packet size 40 bytes Silence indicator (SID) packet size 15 bytes Video traffic
Near real time video [17] Frame per second 15 No. of packets in a frame 8 Min. video frame size 1.5 kilo bytes Packet size Truncated Pareto; K=40 bytes, α =1.2, mean=50 bytes, max=250 bytes Packet inter-arrival time Truncated Pareto; K=2.5 ms, α =1.2, mean= 6 ms, max= 12.5 ms Data traffic Self-similar [18] Packet payload uniformly distributed between [46,1500] bytes T ABLE LTE P ARAMETERS
Parameter Value
Scenario
UMa
Inter - site distance
500 m
System bandwidth
10 MHz
Center frequency
No. of prbs (cid:2)z {|} (cid:9)
50 (48 for data)
No. of prbs in a RC Path loss (cid:2){~(cid:9) model
Non line of sight
Shadowing standard deviation
UE max transmit power ( { (cid:127)€(cid:129) )
24 dBm
Uplink power control (PC) (cid:4)(cid:5)(cid:6) (cid:2)‚ ƒs„ , ‚ R (cid:15) )‚…10 log F† (cid:31) ‡ˆt (cid:9) ‰ for PC { Š For PC -
106 dBm
UE distribution
Poisson point process (PPP)
Simulation duration
10 seconds (10,000 TTIs)
MCS
QPSK, 16 - QAM, 64 - QAM with varying code - rates as given in [16] R ESULTS AND D ISCUSSION
This section illustrates the performance of the pro-posed algorithms, namely DARTS, DAFS and DAFS-PF. In our previous work, we have extensively studied DHAM [10]. In that work, we have compared the perfor-mance of DHAM with that of recursive maximum expan-sion [6], channel aware Hungarian algorithm [7] and buffer based channel dependent scheduler [11]. In [10], we have established that DHAM provides better MAC throughput, buffer build up and fairness as compared to the other scheduling protocols. Therefore, in this paper, we compare our newly proposed algorithms like DARTS, DAFS and DAFS-PF with DHAM only.
Delay aware real - time scheduling: In this sub-section, we compare the performance of DARTS (introduced in Section 3.2) with DHAM. The main parameters to study are the fairness, the MAC throughput, the number of packets delivered by the user having worst channel conditions and the delay. DARTS performs much better in terms of fairness as depicted in Fig. 3a. Fairness is improved in case of DARTS because whenever a user suffers from bad chan-nel conditions for a considerable amount of time, DARTS provides opportunity for them to occupy the channel. Whereas, DHAM only seeks to improve the MAC throughput and as a result generally selects the users with better channel quality. However, it should be noted that the improvement on fairness is obtained without any sacrifice on MAC throughput as seen in Fig. 3b. This hap-pens as DARTS reduces packet drop due to delay. The scheduling principle of DARTS prioritizes users who have packets about to violate the delay constraints. Now, if the input rates of all the users are similar, the poor channel quality users are normally worst hit. Fig. 4a, illustrates the enhancement in the delivery of packets for a user having the worst channel condition due to the de-lay aware scheduling of DARTS.
Figure 3. (a) MAC Fairness vs Network Load (a) MAC Throughput vs Network Load Figure 4. (a) Number of worst user voice packets delivered vs Network Load (b) Voice delay vs Network Load
Finally, in order to prefer the users with higher num-ber of delayed packets, DARTS defers the transmission from the users with better channel quality and therefore increases the average delay. However, DARTS ensures that the delay remains within the delay limits. Fig. 4b shows the effect of DARTS on mean voice delay.
QoS enhancement of multiple classes of traffic:
This sub-section displays the effects of the DAFS and DAFS-PF when multiple classes of traffic are present in the traffic mix. DAFS is the multiclass version of DARTS and therefore, we have not included the results of DARTS in this sub-section. DAFS and DAFS-PF has been com-pared against the performance of DHAM and APASS. Note that, for the result compilation, we have considered the DAFS version with packet drop history (sum of the voice and video metric for 1000 TTIs of recent past). For each of the following figures, we have three sub-plots [a, b and c]. For sub-plot (a), the voice load is made variable while the video and data load are fixed at 1Mbps. For the sub-plot (b), the video load is altered while the voice and data load are fixed at 1Mbps. Finally, for the last sub-plot (c), voice and video load are fixed to 1 Mbps, while data load is varied.
Figure 5. MAC fairness (a) Voice load variable, video and data fixed to 1 Mbps (b) Video load variable, voice and data fixed to 1 Mbps (c) Data load variable, voice and video fixed to 1 Mbps.
Figure 6. MAC throughput (a) Voice load variable, video and data fixed to 1 Mbps (b) Video load variable, voice and data fixed to 1 Mbps (c) Data load variable, voice and video fixed to 1 Mbps
Figure 7. Video packets dropped (a) Voice load variable, video and data fixed to 1 Mbps (b) Video load variable, voice and data fixed to 1 Mbps (c) Data load variable, voice and video fixed to 1 Mbps
As seen in Fig. 5, the MAC fairness provided by DAFS and DAFS-PF is higher than that of both DHAM and APASS. This happens because, both DAFS and DAFS-PF give more priority to the users that have poorer channel conditions. APASS, on the other hand, removes schedulable users in a heuristic manner in its second stage. As a result, the optimal MAC fairness is not at-tained. However, enhancement of MAC fairness results in degradation of MAC throughput as can be seen from Fig. 6. MAC throughput is higher for DHAM as it seeks to maximize MAC throughput. However, DAFS and DAFS- PF seeks to maximize MAC throughput while meeting delay constraints. As a result, the MAC throughput deliv-ered by them is comparatively lower. However, the semi-heuristic nature of APASS makes it sub-optimal even in terms of MAC throughput. Fig. 7 reveals that the DAFS leads to higher video packet drop as compared to DHAM when the percentage of voice traffic is higher in the traffic composition (see Fig. 7a). This directly follows from the fact that DAFS yields lower MAC throughput. Moreover, strict priority sched-uling clears out the voice buffer before transmitting the video packets. As a result, video buffer gets filled up quickly when the voice traffic load is high. DAFS-PF tries to rectify this shortcoming of DAFS by the application of priority flipping. However, DAFS-PF also yields lower MAC throughput than DHAM and hence drops higher number of video packets as compared to DHAM. How-ever, the performance of APASS is poorer than all of our proposals as it ignores several bandwidth starving users because of the usage of heuristic utility functions. On the other hand, when the percentage of voice is low in the traffic mix, DHAM, DAFS and DAFS-PF gives compara-ble performance (see Fig. 7b and 7c).
Figure 8. Number of worst user video packets delivered (a) Voice load variable, video and data fixed to 1 Mbps (b) Video load variable, voice and data fixed to 1 Mbps (c) Data load variable, voice and video fixed to 1 Mbps.
However, when it comes to the number of video packets transmitted by the worst channel user, DAFS and DAFS-PF clearly out performs DHAM. We observe that in this regard, DAFS-PF performs the best because of priori-ty flipping. The comparison can be seen in Fig. 8. The number of video packets delivered by the worst user de-creases as load increases. This is because lack of the transmission opportunities increases the number of pack-et dropped. This happens as all the UEs accumulate large number of packets in their queues when the load is high. However, the video performance of the DAFS-PF is im- proved by borrowing the bandwidth that was to be used for transmitting voice packets in DAFS. Hence, the worst user voice performance is poorer for DAFS-PF than it is for DAFS as shown in Fig. 9. Nevertheless, both the algo-rithms perform better than DHAM for heavy load condi-tions because of their fair scheduling policy. APASS, however, shows significantly poor scheduling for the worst channel user. The primary reason for this is because of the heuristic utility function used in APASS. We be-lieve that APASS is inefficient in a static scenario as the mean path-loss of the users do not change in such a situa-tion. However, our optimal choice of the utility function makes it efficient in a static scenario.
Figure 9. Number of worst user voice packets delivered (a) Voice load variable, video and data fixed to 1 Mbps (b) Video load variable, voice and data fixed to 1 Mbps (c) Data load variable, voice and video fixed to 1 Mbps.
Finally, an interesting trend can be observed in Fig. 9b and Fig. 9c. It may be noted that the number of voice packets delivered when video or data load is varied while keeping the voice load fixed falls till the network load of 5Mbps (Fig. 9b and Fig. 9c). At this moderate load, the worst user does not get enough selection preference as the voice packets are dropped due to delay overshoot. However, as the load increases further, the fairness is in-voked due to higher accumulation of video and data packets. Finally, as the load increases even further, all the users become heavily loaded and compete for the availa-ble bandwidth. Therefore, the voice packet reception from the worst user decreases again. C ONCLUSION
In this paper, we have demonstrated that channel aware scheduling alone in the LTE uplink should not be the de-facto mechanism for resource allocation. In order to utilize the physical resources efficiently, one must make a cross layer optimization including information from the MAC layer. The use of buffer state information while scheduling is obligatory to increase the effective throughput, i.e., the MAC throughput. However, this crude consideration may be rendered unfair when real-time traffic is used. Therefore, we have proposed DARTS for a single class of real time traffic, DAFS and DAFS-PF for multiple classes of real-time traf-fic. These advanced low complexity scheduling algo-rithms produce optimal results while successfully en-hancing the fairness among users. The novelty of the al-gorithms lies in the usage of packet drop due to delay constraints in place of head of the line delay. Further, these algorithms make use of the long buffer status re-ports to transmit the packet drop value from the UEs to the eNodeB. This relieves the system from transmission of heavy control information. Finally, priority flipping, in-troduced in DAFS-PF, boosts video performance and re-duces data starvation in appropriate scenarios. Extensive simulation studies have confirmed that the LTE uplink performance can be improved significantly by incorporating the proposed schedulers in the LTE eNodeB. R EFERENCES [1]
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Atri Mukhopadhyay received his M.Tech degree in Distributed and Mobile Computing from Jadavpur University, India. He is presently working towards Ph.D. from GSSST, Indian Institute of Technology, Kharagpur, India. His research interests include wireless-optical integrated networks, optical access networks and wireless access networks.