An Examination of the Benefits of Scalable TTI for Heterogeneous Traffic Management in 5G Networks
Emmanouil Fountoulakis, Nikolaos Pappas, Qi Liao, Vinay Suryaprakash, Di Yuan
11 An Examination of the Benefits of Scalable TTI forHeterogeneous Traffic Management in 5G Networks
Emmanouil Fountoulakis , Nikolaos Pappas , Qi Liao , Vinay Suryaprakash , Di Yuan Department of Science and Technology, Link ¨oping University, Sweden Nokia Bell Labs, Stuttgart, GermanyE–mails: { emmanouil.fountoulakis, nikolaos.pappas, di.yuan } @liu.se { qi.liao, vinay.suryaprakash } @nokia-bell-labs.com AbstractThe rapid growth in the number and variety of connected devices requires 5G wireless systems to copewith a very heterogeneous traffic mix. As a consequence, the use of a fixed transmission time interval (TTI)during transmission is not necessarily the most efficacious method when heterogeneous traffic types needto be simultaneously serviced. This work analyzes the benefits of scheduling based on exploiting scalableTTI, where the channel assignment and the TTI duration are adapted to the deadlines and requirementsof different services. We formulate an optimization problem by taking individual service requirements intoconsideration. We then prove that the optimization problem is NP-hard and provide a heuristic algorithm,which provides an effective solution to the problem. Numerical results show that our proposed algorithm iscapable of finding near-optimal solutions to meet the latency requirements of mission critical communicationservices, while providing a good throughput performance for mobile broadband services.Index Terms5G, scalable TTI, deadline-constrained traffic, low latency, channel allocation, service-centric scheduler
I. I
NTRODUCTION
The statement, “Future wireless access will extend beyond people, to support connectivity for anythingthat may benefit from being connected.”, by the authors of [1] has far reaching implications. This entailsthat a variety of new autonomous devices, such as drones, sensors, etc., will communicate using thesame network that simultaneously has to serve conventional mobile broadband (MBB) services. Thus,next generation wireless communications systems will be characterized by their service requirementheterogeneity [2]. A characteristic example of services, which have requirements vastly different fromMBB services, are those that fall under the category of machine type communications (MTC) [3]. Twosubcategories of MTC services are the mission critical communications (MCC) and the massive machinetype communications (MMC). MCC services are characterized by small packets and require ultra lowlatency ( ≤ ms, [1]) and high reliability [4]. On the other hand, MMC envisions tens of billions ofconnected devices [1]. Therefore, it is not far-fetched to assume that the use of a fixed TTI length forcatering to such a diverse set of services could be suboptimal. For traffic types in which the ratio betweenthe size of signaling and data is greater than or equal to , fixed TTI leads to a significant wastage ofresources and – as a result – inefficient communications. The promise of scalable TTI as a potentialsolution was demonstrated in [5], where the TTI length could be scaled according to the traffic type.To support a mix of services with heterogeneous requirements, in [3] and [6] the authors propose aflexible frame structure in frequency division dublex (FDD) networks. In these works, the delay constraintsare reverse engineered based on the channel state information and the delay budgets. Along similar lines,the authors in [7] apply the variable frame structure in the context of millimeter wave communications.However, these works aim to prioritize active services with strict latency requirements, while sacrificing a r X i v : . [ c s . I T ] M a y the throughput of mobile broadband users. In a recent work [5], scalable TTI lengths are introducedin dynamic time division duplex (TDD) mode in order to consider the requirements of each individualservice and provide a good trade-off between heterogeneous performance metrics (with respect to theircorresponding traffic demands and latency requirements). Moreover, the dynamic TDD scheme offersgreater flexibility than the FDD scheme, in terms of adaptability to an asymmetry in UL and DL traffic.However, none of the works mentioned above jointly considers dynamic TTI length adaptation and channelallocation. In addition to scheduling flexibility in the time domain, jointly considering scalable TTI andchannel allocation provides a more flexible frame structure, which is better at exploiting channel diversityand improving spectral efficiency.In this paper, we aim to develop a scheduling approach that strives to fulfill the (service) deadlinesand requirements of different types of services by scaling the length of the TTI to be used. To thisend, we formulate an optimization problem whose solution provides the appropriate TTI length and thechannel allocation for each service. We then prove that the optimization problem formulated is NP-hard.Therefore, in order to have a scheduler that works in polynomial time, we propose a greedy algorithm thatfinds an approximate solution to the optimization problem. Numerical results show that the formulatedoptimization problem tries to cater to all MCC services within their latency requirements, while providinga higher throughput for MBB services in comparison to the other methods commonly considered. Theyalso indicate that the improvement in performance provided by our formulation over the shortest deadlinefirst scheduler (SDFS) increases as the number of active MCC services increases.II. S YSTEM M ODEL
We consider a single cell of an FDD network in downlink mode . We also consider services, each witha deadline within which all their requirements must be met. Henceforth, we will use the term servicesrather than users in recognition of the fact that a user can request more than one service. In this paper,we assume discretized time and ‘ one time unit ’ refers to the minimum amount of time during which atransmission can occur. Let the TTIs be indexed in the time domain by n ∈ N . The length of each TTI ∆( n ) , ∀ n ∈ N is scalable and can be selected from a finite set ∆( n ) ∈ { , , . . . , L } , where L ∈ N is thelargest number of time units that can be assigned to a particular TTI. The active set of services at thebeginning of the n -th TTI is denoted by S n with cardinality |S n | .Let K (cid:44) { , , . . . , K } ⊂ N be the set of available channels with cardinality |K| , and assume thatthe same TTI size is retained for all the channels. Each service s ∈ S n can be allocated to a number ofchannels. We use the vector a s ( n ) ∈ { , } |K| to denote the allocation of channels to a service s . The i -thelement of a s ( n ) , a i,s ( n ) , takes the value one if the i -th channel is assigned to the service s during the n -th TTI, and takes the value zero otherwise. Let N Z s ( n ) denote the set of non-zero elements of vector a s ( n ) . Let the channel allocation for all services be collected in a binary matrix A ( n ) ∈ { , } |K|×|S n | ,where the s -th column is a s ( n ) . Each channel can be assigned up to one service within a TTI and thus,we have the following constraint (cid:88) s ∈S n a i,s ( n ) ≤ , ∀ i ∈ K , ∀ n ∈ N . (1)Each channel i has a known channel state information (CSI) for every service s . The CSI in the i -thchannel for the s -th service in the n -th TTI is a tuple defined as CSI i,s ( n ) = ( R i,s ( n ) , T i,s ( n )) . In this tuple, R i,s denotes the transmission rate of the s -th service over the i -th channel (in bits/one timeunit) that can be sustained without errors for T i,s time units, if the i -th channel is assigned to s . Note thatthe CSI of a channel still changes from one TTI to another. In this work, we assume that the downlink resources are always available since we consider an FDD system. However, the same formulationcan also be applied to a TDD system, depending on whether the carriers are configured in uplink or downlink mode during a given timeperiod.
At the beginning of the n -th TTI, each service s has a known data requirement denoted by Q s ( n − .Then, we denote Q s ( n ) as the amount of data (in bits) that still needs to be served at the end of the n -thTTI. The evolution of the backlog can be described by Q s ( n ) (cid:44) (cid:34) Q s ( n − − (∆( n ) − δ ) (cid:88) i ∈K a i,s ( n ) R i,s ( n ) (cid:35) + , (2)where [ · ] + (cid:44) max { , ·} and δ is the fraction of a time unit required for the transmission of the signalingoverhead. We assume that δ is less than or equal to one time unit. Moreover, each service has a specificdeadline before which the data has to be delivered. If a service is not completely served before thedeadline, the system fails to meet its requirements and the service is dropped. This deadline is denotedby D s ( n ) , and defined as D s ( n ) (cid:44) [ D s ( n − − ∆( n )] + . (3)If Q s ( n ) (cid:54) = 0 and D s ( n ) = 0 , the service s is dropped from the system, whereas if Q s ( n ) = 0 and D s ( n ) ≥ , the service s is completely served and exits the system. Additionally, we define the “emptyingrate”, E s ( n ) , of a service s at the end of the n -th TTI by E s ( n ) (cid:44) Q s ( n − − Q s ( n ) Q s ( n − , (4)where E s ( n ) ∈ [0 , , represents the ratio between the data served within the n -th TTI and the amount ofdata remaining at the end of the ( n − -th TTI. This implies: the larger the emptying rate, the faster thedata is served with respect to what was remaining at the end of the previous TTI. For example, if service s is completely served at the end of the third TTI, then Q s (3) = 0 and E s (3) = 1 ; on the other hand, if s is not served at all during the third TTI, then Q s (2) = Q s (3) and thus, E s (3) = 0 .III. P ROBLEM F ORMULATION
At the n -th TTI, the optimization variables for the TTI length and the channel allocation are { ∆( n ) , A ( n ) } ,respectively. Our objective is to address the trade-off between the throughput performance and numberof dropped services. To this end, we develop a scheduling scheme that will be able to either prioritizeservices with short deadlines, or(/and) services that can be completely served during the current round ofscheduling. A. Utility function
We define our utility function as U ( n ) (cid:44) (cid:88) s ∈S n W s ( n ) E s ( n ) , (5)where E s ( n ) is the emptying rate, and the weight W s (cid:44) D s ( n − . Note that W s increases when the D s ( n − decreases, i.e., its value increases if the deadline is soon to expire. Since we consider discretetime, the smallest value D s ( n − can attain is one time unit. Therefore, the maximum value of W s isone and as a result, the maximum value of function U ( n ) is equal to |S n | . Hence, the function providesa higher reward when the following types of services are served: i) those having urgent deadlines; and,ii) those that can be served with higher emptying rates. B. Optimization Problem
Although the utility U ( n ) in (5) is designed to prioritize services with urgent deadlines, U ( n ) alonecannot guarantee that services, which can be completely served during the current round of schedulingare chosen. Therefore, we formulate the optimization problem by augmenting the utility function and byintroducing additional constraints, as given below. max ∆( n ) , A ( n ) U ( n ) + θ ( n ) (6a)s. t. ∆( n ) ≤ min s ∈S n min i ∈N Z s ( n ) T i,s ( n ) , (6b) (cid:88) s ∈S n a i,s ( n ) ≤ , ∀ i ∈ K , (6c) ∆ ( n ) ∈ { , . . . , L } , (6d) A ( n ) ∈ { , } |K|×|S n | , (6e) θ ( n ) = M (cid:88) s ∈S n { Q s ( n )=0 } , (6f)where M = ( |S n | − . Moreover, { B } is the indicator function which takes the value one if the event B occurs, and the value zero otherwise. For the rest of this paper, we refer to the problem above as scalable-TTI enabled channel allocation STCA. The objective function (6a) is the sum of the utility function (5)and an additional reward θ ( n ) . The function θ ( n ) , defined in (6f), is equal to the product of a constant M and the number of completely satisfied services at the end of the current TTI. This, therefore, ensuresthat the number of completely served services is included in the objective function (6a). Furthermore, θ ( n ) also ensures that if at least one service is completely served, the value it takes in the correspondingterm of the objective function (6a) is greater than the sum of the other ( |S n | − terms of the objectivefunction. As a result, we prioritize services that can be completely served after the current schedulinginstance.Additionally, constraint (6b) ensures that the selected TTI size does not violate the minimum TTI sizefor a given channel and service. Constraint (6c) ensures that a channel can be assigned to up to oneservice. IV. C OMPLEXITY
This section addresses the complexity of the optimization problem. Specifically, we prove that theoptimization problem, as defined in Section III, is NP-hard. However, as shown later on in Theorem 2,the problem admits a polynomial-time algorithm guaranteeing optimality, if flat channels are assumed.By flat channels, we mean that for each service, the channel gains are the same for all channels within agiven TTI.
Theorem 1.
STCA is NP-hard.Proof.
We prove that the decision version of the STCA problem is NP-complete by a polynomial-timereduction to and from the Partition Problem (PP) in three steps, [8]. The decision version of the STCAproblem can be stated as:
Given a set of services S n , the backlogs Q s ( n − , the deadlines D s ( n − , a set of channels K , andthe achievable rates R i,s ( n ) , ∀ i ∈ K and ∀ s ∈ S n , is there a solution of the given STCA instance suchthat the value of the objective function is at least f , where f is a given positive number?Step 1 : We prove that the STCA problem belongs to the NP class of problems, i.e. given an STCA instance,a positive answer and its associated solution, it takes polynomial time to verify whether the answer to thequestion posed is indeed YES. It is a plain to see that, given a solution, computing U ( n ) + θ ( n ) takespolynomial time. Therefore, STCA is in the NP class of problems. Step 2 : We now show that there is a polynomial-time reduction from the PP to the STCA problem. Inthe PP, for a set of positive integers { p , . . . , p m } , the task is to determine whether or not this set can bepartitioned into two subsets of equal sums, i.e. (cid:80) i ∈A (cid:48) p i = (cid:80) i ∈A\A (cid:48) p i , where A = { , . . . , m } and A (cid:48) ⊂ A .Without loss of generality, we can assume that (cid:80) i ∈A p i is even. Then, given an instance of the PP, we candefine an instance of the STCA problem as follows: • S n = { , } , = ⇒ |S n | = 2 . |K| = |A| . • D s ( n −
1) = 1 time unit, ∀ s ∈ S n . • ∆( n ) = 1 time unit. • δ = 0 . R i,s ( n ) = p i , ∀ s ∈ S n , ∀ i ∈ A . • Q s ( n ) = (cid:80) i ∈A p i , ∀ s ∈ S n .Based on the instance defined above, the value of f in the decision version of this STCA instance is setto , i.e., f = 4 . From the assignments above, there is a one-to-one mapping between the elements in thePP and the channels in the STCA problem. In particular, we associate the i -th element in A with the i -thelement in K . Therefore, the above definition clearly represents a polynomial-time reduction. Step 3 : We now prove that the PP instance has the answer YES if and only if the answer to the definedSTCA decision instance is YES. If the answer to the PP instance is YES, there are two sets A (cid:48) and A \ A (cid:48) , such that (cid:80) i ∈A (cid:48) p i = (cid:80) i ∈A\A (cid:48) p i = (cid:80) i ∈A p i . We assign the channels corresponding to the set A (cid:48) to oneservice, and the channels corresponding to the set A \ A (cid:48) to the other. Hence, for the STCA instance,we have (cid:80) i ∈A (cid:48) R i, = (cid:80) i ∈A\A (cid:48) R i, = (cid:80) i ∈A p i . Since Q s ( n ) = (cid:80) i ∈A p i , ∀ s ∈ S n , both services are completelyserved and therefore, f = 4 . Hence, the instance above is a YES instance of the defined STCA decisionproblem.Conversely, if the answer to the defined STCA decision instance is YES, there are two sets K (cid:48) and K \ K (cid:48) which correspond to the channel assignments for the services one and two, respectively. Since theanswer is YES, there is a solution such that the value of the objective function is equal to . Note thatthis value can be reached if and only if both services are completely served. Hence, we have (cid:88) i ∈K (cid:48) R i, ( n ) ≥ (cid:88) i ∈A p i , (7) (cid:88) i ∈K\K (cid:48) R i, ( n ) ≥ (cid:88) i ∈A p i . (8)We also have, by definition, that (cid:80) i ∈K R i,s ( n ) = (cid:80) i ∈A p i , for s ∈ { , } , and R i, ( n ) = R i, ( n ) = p i , ∀ i .Therefore, the conditions (7) and (8) hold if and only if they are equal. Hence, (cid:80) i ∈K (cid:48) p i = (cid:80) i ∈K\K (cid:48) p i = (cid:80) i ∈K p i ,and {K , K \ K (cid:48) } is a feasible partition. This establishes the NP-completeness of the decision version ofthe STCA problem. Therefore, the STCA problem is NP-hard.This leads us to the proof that the global optimum of STCA can be computed in polynomial time forthe special case of flat channels.
Theorem 2.
The global optimum of STCA can be computed in polynomial time for flat channels.Proof.
If we have K flat channels, then CSI k,s i = CSI l,s j , for all channels k and l , and for all services s i and s j . Let g sk denote the value of the objective function when k channels are allocated to service s , i.e. g sk = (cid:40) W s ( n ) + M, if Q s ( n ) = 0 ≡ E s ( n ) = 1 ,W s ( n ) E s ( n ) , otherwise . (9) Moreover, if there is no channel assigned to the service s , then g s = 0 . Let h s ( i ) denote the objectivefunction value of optimally allocating i channels to services { , . . . , s } . The optimal objective value canbe computed by the recursive function h s ( k ) = max k =0 , ,...,K { g sk + h s − ( K − k ) } . (10)We then construct a |S n |× K matrix whose elements are computed using (10). The ( s, k ) -th element of thematrix includes the optimal value of the objective function for services { , . . . , s } using k channels. Hence,the ( |S n | , K ) -th element gives the value of the optimum solution of the entire optimization problem.For the first row of the matrix, computing the entries h (1) , . . . , h ( k ) in the given order are straight-forward, and each entry requires a computational complexity of O (1) . Each element of the s -th rowrequires K (cid:80) i =1 i = K ( K + 1) / computations. Hence, the computational complexity that is required foreach row is O ( K ) and thus, the total computational complexity is O ( |S n | K ) . Therefore, the optimumsolution of the STCA problem, in the case of flat channels, can be computed using dynamic programmingin polynomial time. V. I NTEGER L INEAR P ROGRAMING F ORMULATION
In this section, we develop an Integer Linear Program (ILP) in order to compute the optimal solutionof the STCA problem, which enables a more detailed study of the performance of scalable TTI. First, wesolve the problem in (6a) with a fixed TTI length as an input. Note that the problem is solved for eachviable TTI length separately. Then, we compare the value of the objective function for all the TTI lengthsconsidered, and subsequently select the TTI length and the channel assignment for which the objectivefunction is maximized. The pair { ∆( n ) , A ( n ) } for which the objective function in (6a) is maximized isthe optimal solution. It should be noted that, for each possible TTI length, if the TTI length is greater thana given service’s deadline, we remove the corresponding service from the optimization problem; thereby,considering the service dropped. In other words, the services whose deadlines will expire despite choosingthe optimal ∆ (denoted by ∆ (cid:48) ) have a utility equal to zero. Thus, for each fixed ∆ (cid:48) , we consider the setof services { s ∈ S n : D s ( n − ≥ ∆ (cid:48) } .In this section, we omit the index n for notational brevity and redefine some of the parameters asfollows: • Q (cid:48) s – the data backlog of s during the current TTI. • W (cid:48) s = W s Q (cid:48) s . • β s – amount of data served to the service s at the end of the current TTI. • R (cid:48) i,s = (∆ − δ ) R i,s is the amount of data that could be transmitted to service s , if the channel i isassigned to it. • Y s = (cid:40) , if the service s is completely served, , otherwise. • D (cid:48) s – the deadline of service s after the ( n − -th TTI. • S ∆ (cid:48) = { s ∈ S n : D (cid:48) s ≥ ∆ (cid:48) } .The rest of the notations remain unchanged. The optimization problem can then be formulated as the following ILP for a given W s ∈ R + and ∆ (cid:48) . max A (cid:80) s ∈S ∆ (cid:48) W (cid:48) s β s + M (cid:80) s ∈S ∆ (cid:48) Y s (11a)s. t. ∆ (cid:48) − T i,s ≤ J (1 − a i,s ) , ∀ i ∈ K , ∀ s ∈ S ∆ (cid:48) , (11b) (cid:80) s ∈S ∆ (cid:48) a i,s ≤ , ∀ i ∈ K , (11c) β s ≤ (cid:80) i ∈K R (cid:48) i,s a i,s , ∀ s ∈ S ∆ (cid:48) , (11d) Y s ≤ β s Q (cid:48) s ≤ , ∀ s ∈ S ∆ (cid:48) , (11e)where the constant J (cid:29) L in (11b) guarantees that a i,s = 0 if T i,s < ∆ (cid:48) . The constraint (11c) ensuresthat each channel is assigned up to one service and (11d) makes sure that the maximum value β s canattain is the amount of data remaining for service s . Therefore, if the service s is completely served, thecorresponding term in (11a) takes the maximum value, which is equal to W s . Note that the ratio β s Q (cid:48) s in(11e) represents the emptying rate in (4). Additionally, if s is completely served, constraint (11e) ensuresthat Y s is assigned a value equal to one. VI. A LGORITHM
Algorithm 1:
CAST algorithm G max ← −∞ , W s = D s ( n − , ∀ s ∈ S for ∆ (cid:48) = 1 : L do A (cid:48) ← K ×|S| , S (cid:48) ← S , Q (cid:48) s ← Q s if D s ( n − − ∆ (cid:48) < then S (cid:48) ← S \ { s } for i ∈ K do g max ← −∞ for s ∈ S (cid:48) do if ∆ (cid:48) ≤ T i,s then Q temp ← [ Q (cid:48) s − (∆ (cid:48) − δ ) R i,s ] + E (cid:48) s ← Q s ( n − − Q temp Q s ( n − g ← W s E (cid:48) s + M { Q temp =0 } if g > g max then s max ← s , g max ← g Q s max ← Q temp if Q s max = 0 then S (cid:48) ← S \ { s max } else A (cid:48) i,s ← G ← G + g max , A (cid:48) i,s max ← if G > G max then A max ← A (cid:48) ∆ max ← ∆ (cid:48) A ( n ) ← A max , ∆( n ) ← ∆ max In order to have a polynomial time scheduling algorithm, we propose a heuristic called channel allocationwith scalable TTI (CAST) algorithm. For each channel i ∈ K , the CAST algorithm finds the service s ∈ S n ,which has the maximum corresponding value of the objective function (6a) – should the channel i beassigned to service s . The algorithm calculates the objective function for each possible TTI length, andselects the channel assignment and the TTI length for which the objective function is maximized.The CAST algorithm decides the channel assignment for each TTI length in two steps. During the firststep, the algorithm excludes the services whose deadlines cannot be met (lines 4 – 5). The variable g , whose value is calculated in lines 9 – 12, is the objective function value, if the channel i is assigned tothe service s . Note that a channel i can be assigned to service s only if the TTI length ∆ (cid:48) is less thanthe duration T i,s within which an error-free computation of the rate is possible (cf. line 9). During thesecond step, the algorithm allocates each channel to a corresponding service with the maximum value ofthe objective function (cf. lines 14 – 15) and removes the service if it is completely served (lines 16 –17). The algorithm then compares the value of the objective function for each possible TTI length andselects the channel assignment as well as the TTI length maximizing the value of the objective function(lines 21 – 24). Based on the description of ILP above, the complexity of the CAST algorithm is foundto be O ( |K||S n | L ) . VII. N UMERICAL R ESULTS
In this section, we compare the performance of the CAST algorithm with the optimal solution (OS) forthe STCA problem. Additionally, we also compare our approach with a simpler version of the shortestdeadline first scheduler (SDFS) proposed by the authors in [6]. The above mentioned comparisons areundertaken using the simulations based on the parameters that follow.We consider one time unit to be equal to . ms, and the TTI length can be selected from a finiteset ∆( n ) ∈ { . ms , . ms , . . . , ms } in a single cell scenario where the FDD is in downlink mode .We also assume that the transmission of control signaling requires δ = 0 . ms per TTI (regardlessof the length of the TTI chosen). We consider a system with an MHz bandwidth that works on afrequency selective channel with a coherence bandwidth of . MHz. The achievable rate for a service s in the i -th channel during the n -th TTI is computed using the Shannon formula and is given by R i,s ( n ) = B log (cid:0) | h i,s ( n ) | SN (cid:1) , where the channel gains h i,s ( n ) are distributed as a zero-mean complexGaussian with variance σ , i.e., h i,s ( n ) ∼ CN (0 , σ ) , S is the transmit power, N is the noise power, and B is the bandwidth of each channel, i.e., B = 0 . MHz. The average value of the signal-to-noise ratio(SNR) is equal to dB. Moreover, we consider that the base station caters to services generated by threeMCC sources and one MBB source. Each source generates services per time unit ( . ms) according to aBernoulli distribution with probability r MCC and r MBB for MCC sources and the MBB source, respectively.Lastly, each MCC service has a demand of bytes and deadline of ms, and each MBB service has ademand of bytes and a deadline of ms. In the following paragraphs, we study the behavior of thealgorithms proposed for various values of r MCC , while the probability of MBB service arrivals is constantand equal to 0.2, i.e., r MBB = 0 . . Average number of MCC services/time unit (0.1 ms) S e r v e d M CC s e r v i ce s [ % ] STCA (scalable TTI) - OSSTCA (scalable TTI) - CASTSTCA ( ∆ = 0 . ∆ = 0 . ∆ = 0 . ∆ = 0 . Fig. 1: Variations in MCC services. Note that ∆( n ) here is presented with the units ’milliseconds’ for improved readability. The value of ∆( n ) in milliseconds is obtained by multiplyingthe original ∆( n ) with the duration of one time unit ( . ms). Average number of MCC services/time unit (0.1 ms) T h r o u g hpu t o f M BB s e r v i ce s [ M b i t s / s ] STCA (scalable TTI) - OSSTCA (scalable TTI) - CASTSTCA ( ∆ = 0 . ∆ = 0 . ∆ = 0 . ∆ = 0 . Fig. 2: Variations in the throughputs of MBB services.
Average number of MCC services/time unit (0.1 ms) S e r v e d M BB s e r v i ce s [ % ] STCA (scalable TTI) - OSSTCA (scalable TTI) - CASTSTCA ( ∆ = 0 . ∆ = 0 . ∆ = 0 . ∆ = 0 . Fig. 3: Variations in MBB services.Fig. 1 depicts the variations in the percentage of MCC services dealt with as the average number ofMCC service requests per time unit ( . ms) increases. It documents the aforementioned variations forboth the optimal solution and the heuristic of the STCA in scenarios where the TTI lengths are scalableand fixed, as well as the variations seen in the behavior of the SDFS. This figure indicates that a schedulerusing the STCA with short but fixed TTI lengths outperforms the one using the STCA with scalable TTIas well as the SDFS. The reason why the STCA with short, fixed TTI outperforms the STCA with scalableTTI is because the latter tends to select longer TTI lengths in order to be able to completely serve as manyservices as possible during each scheduling period. This sort of selection implies that a greater portionof the MCC services end up being dropped. However, as the arrival rate of MCC services continues toincrease, the STCA with scalable TTI starts to select shorter TTI lengths; thereby, resulting in the increasein the percentage of MCC services catered to between . and MCC arrivals / . ms before eventuallydecreasing beyond . MCC services / . ms. It is noteworthy that the STCA with scalable TTI eventuallyoutperforms the STCA with fixed TTI, i.e., beyond . MCC services / . ms.As commonly known, the amount of signaling overhead increases quite substantially when shorter TTIlengths are selected. The cost of an increase in the signaling overhead is born a decrease in the throughputdelivered to the MBB services. Fig. 2 demonstrates the variations in the throughput of the MBB servicesas the average number of MCC service requests / . ms increases. Clearly, of the methods considered, the SDFS is the one that is most significantly affected. This figure also indicates that, though the MBB servicessee an inevitable drop in their throughput, the STCA with scalable TTI is able to cope much better thanthe STCA with short, fixed TTI – especially when the average number of MCC service requests / . msis greater than . . A reason why the STCA with scalable TTI outperforms the STCA with short, fixedTTI is because of its ability to contain (and regulate) the amount time spent in transmitting the controlsignaling more effectively.Lastly, Fig. 3 – as in Fig. 2 – depicts the unavoidable decrease in the percentage of MBB servicessatisfied when the average number of MCC service requests / . ms increases. It does, however, highlightthe fact that the STCA with scalable TTI is able to serve a far greater percentage of MBB serviceswhen compared to the others in the face of increasing MCC service requests / . ms. This behavior can,once again, be attributed to the fact the STCA with scalable TTI can control the fraction of time spenttransmitting the control signaling by periodically choosing larger TTI lengths and thereby, ensuring thatMBB services are also furnished with the resources they need. Also, the results illustrate that there is avisible gap between the performance of the CAST algorithm and the OS, though the CAST algorithmsignificantly outperforms the SDFS. This gap is expected because of the low complexity of the CASTalgorithm.Overall, when one considers all the results collectively, it can be said that a scheduler which jointlyconsiders scalable TTI and channel allocation into account is better at being able to handle trafficheterogeneity and has the ability to improve the spectral efficiency of individual service types.VIII. C ONCLUSIONS
In this paper, at each scheduling time, we propose a joint optimization of the TTI lengths and the channelallocation depending on the traffic type. The joint optimization problem formulated is then proven to beNP-hard due to which we provide a heuristic akin to a greedy algorithm. However, for flat channels,we also demonstrate that the problem admits a polynomial-time solution that guarantees optimality. Theoptimization problem and its heuristic are then compared not only with one another for the cases of fixedand scalable TTI lengths, but also with the shortest deadline first scheduler. These evaluations illustratethat our proposal of a joint optimization of TTI lengths and channel allocation is better equipped to handletraffic heterogeneity and provide improved spectral efficiency, due to its ability to regulate the amount oftime spent on control signal transmissions and maximize the number of services satisfied.IX. A
CKNOWLEDGMENT
The authors would like to thank Dr. Ilaria Malanchini for numerous fruitful discussions and her valuablesuggestions. This work has been supported by the European Union’s Horizon 2020 research and innovationprogramme under the Marie Skłodowska-Curie grant agreement No. .R EFERENCES [1] E. Dahlman, G. Mildh, S. Parkvall, J. Peisa, J. Sachs, and Y. Sel´en, “5G radio access,”
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