Prajwal Osti

Analysis of PDCCH performance for M2M traffic in LTE

As Long-Term Evolution (LTE) is starting to be widely deployed, the volume of machine-to-machine (M2M) traffic is increasing very rapidly. From the M2M traffic point of view, one of the issues to be addressed is the overload of the random access channel. The limitation in the physical downlink control channel (PDCCH) resources may severely constrain the number of devices that an LTE Evolved Node B (eNB) can serve. We develop a Markov model that describes the evolution of the Message 4 queue in the eNB formed by several users performing the random access procedure simultaneously, and then, we study its stability and performance. Our model explicitly takes into account the four initial steps in the random access procedure. By utilizing the model, we are able to determine the stability limit of the system, which defines the maximum throughput and the probability of failure of the random access procedure due to different causes. We observe that the sharing of the PDCCH resources between Messages 2 and 4 with different priorities makes the performance of the whole random access procedure deteriorate very rapidly near the stability limit. However, we can extend the maximum throughput and improve the overall performance by increasing the PDCCH resource size. Furthermore, we estimate the upper limit of the number of devices that can be served by an LTE eNB and determine the minimum PDCCH resource size needed to satisfy a given traffic demand.

On the optimal trade-off between SRPT and opportunistic scheduling

We consider service systems where new jobs not only increase the load but also improve the service ability of such a system, cf. opportunistic scheduling gain in wireless systems. We study the optimal trade-off between the SRPT (Shortest Remaining Processing Time) discipline and opportunistic scheduling in the systems characterized by compact and symmetric capacity regions. The objective is to minimize the mean delay in a transient setting where all jobs are available at time 0 and no new jobs arrive thereafter. Our main result gives conditions under which the optimal rate vector does not depend on the sizes of the jobs as long as their order (in size) remains the same. In addition, it shows that in this case the optimal policy applies the SRPT principle serving the shortest job with the highest rate of the optimal rate vector, the second shortest with the second highest rate etc. We also give a recursive algorithm to determine both the optimal rate vector and the minimum mean delay. In some special cases, the rate vector, as well as the minimum mean delay, have even explicit expressions as demonstrated in the paper. For the general case, we derive both an upper bound and a lower bound of the minimum mean delay.

Whittle Index Approach to Size-aware Scheduling with Time-varying Channels

We consider the optimal opportunistic scheduling problem for downlink data traffic in a wireless cell with time-varying channels. The scheduler itself operates in a very fast timescale of milliseconds, but the objective function is related to minimizing the holding costs in a much longer timescale, at the so-called flow level. The Whittle index approach is a powerful tool in this context, since it renders the flow level optimization problem with heterogeneous users tractable. Until now, this approach has been applied to the opportunistic scheduling problem to generate non-anticipating index policies that may depend on the amount of attained service but do not utilize the exact size information. In this paper, we produce a size-aware (i.e., anticipating) index policy by applying the Whittle index approach in a novel way. By a numerical study based on simulations, we demonstrate that the resulting size-aware index policy systematically improves performance. As a side result, we show that the opportunistic scheduling problem is indexable when the file sizes follow the Pascal distribution, and we derive the corresponding Whittle index, which generalizes earlier results.

Load Balancing for M2M Random Access in LTE HetNets

In heterogeneous LTE networks, an incoming user can either join the femto or the macro base station at the random access stage. We consider a system that has a single macro base station and a number of femtocells in its coverage area. We study the problem of optimally choosing either the femto or the macro station based on the knowledge of the traffic arrival rate and the number of backlogged users in both cells. In this paper, we derive the optimal static policy of choosing the base stations that minimizes the average access delay. We also develop various dynamic policies based on the information about the arrivals and backlogged users, and compare their performance against each other and with the optimal static policy. We observe that some of these dynamic policies give very good performance, which provides a lower bound of performance. In addition, a dynamic policy that utilizes only the backlog levels, although not always as good as the optimal static policy, is robust and still stable for a wide range of arrival rates.

Optimal size-based opportunistic scheduler for wireless systems

Modern wireless cellular systems are able to utilize the opportunistic scheduling gain originating from the variability in the users’ channel conditions. By favoring users with good instantaneous channel conditions, the service capacity of the system can be increased with the number of users. On the other hand, for service systems with fixed service capacity, the system performance can be optimized by utilizing the size information. Combining the advantages of size-based scheduling with opportunistic scheduling gain has proven to be a challenging task. In this paper, we consider scheduling of data traffic (finite-size elastic flows) in wireless cellular systems. Assuming that the channel conditions for different users are independent and identically distributed, we show how to optimally combine opportunistic and size-based scheduling in the transient setting with all flows available at time 0. More specifically, by utilizing the time scale separation assumption, we develop a recursive algorithm that produces the optimal long-run service rate vectors within the corresponding capacity regions. We also prove that the optimal operating policy applies the SRPT-FM principle, i.e., the shortest flow is served with the highest rate of the optimal rate vector, the second shortest with the second highest rate, etc. Moreover, we determine explicitly how to implement the optimal rate vectors in the actual time slot level opportunistic scheduler. In addition to the transient setting, we explore the dynamic case with randomly arriving flows under illustrative channel scenarios by simulations. Interestingly, the scheduling policy that is optimal for the transient setting can be improved in the dynamic case under high traffic load by applying a rate-based priority scheduler that breaks the ties based on the SRPT principle.

Data aggregation in capillary networks for machine-to-machine communications

As machine-to-machine applications using cellular systems become pervasive, it is an important concern that their deployment does not jeopardize the performance of the cellular systems. Support for a massive number of machines brings technical challenges affecting the performance of the random access channel and efficiency of radio resource allocation. Capillary networks are considered as an extensions to the cellular systems for providing large-scale connectivity. This paper proposes an aggregation scheme for capillary networks connected to the LTE network to improve their communication efficiency. A gateway, an intermediate unit between machines and the base station, aggregates packets from the machines during a predefined time, and then delivers them to the LTE network. In addition, this paper analyzes the trade-offs between random access interaction, resource allocation, and communication latency. Results reveals that accepting the extra latency for accumulating packets can significantly reduce the random access requests and the required resources for the data transmissions.

Flow-level modeling and optimization of intercell coordination with dynamic TDD

We study the intercell coordination problem between two interfering cells combined with dynamic time-division duplexing (TDD). In dynamic TDD, each station selects in each time slot whether it is serving uplink (u) or downlink (d) traffic. Thus, the system has four possible operation modes (uu, ud, du, dd). The amount of intercell interference between the stations clearly depends on the operation mode. We consider a flow-level model where traffic consists of elastic data flows in both cells (cells 1 and 2) and in both directions (uplink and downlink). We first characterize the maximal stability region, and then determine the optimal static (i.e., state-independent) policy. Our main objective is to analyze the potential gains from applying dynamic (i.e., state-dependent) policies, where the chosen operation mode depends on the instantaneous state of the system. To this end, motivated by certain stochastic optimality results in the literature, we define several priority policies. As a reference policy, we have the well-known max-weight policy, and we also develop another dynamic policy by applying the policy iteration algorithm. Notably we prove that certain simple priority policies are, in fact, stochastically optimal in some special cases, but which policy is optimal depends on the setting. To study the exact performance gains achieved by the dynamic policies, we perform extensive simulations. While our stochastic optimality results require exponential service times, in the simulations, we also study the impact of nonexponential service times and consider a physical model where the service time distribution is determined by the joint distribution of flow sizes and the random location of the corresponding user in the cell area. The max-weight policy is, as expected, performing well but the various priority policies are sometimes better and even optimal. Jointly the results indicate that dynamic policies give significant performance gains compared with the optimal static policy.

Optimal intercell coordination for multiple user classes with elastic traffic

We consider the intercell coordination problem between two neighboring cells, assuming that the traffic in the system consists of elastic downlink data flows. In this case, there is an option of completely switching off one base station at certain times, which reduces interference and enables a higher service rate in the neighboring base station. We use a flow level queueing model to describe the evolution of the system based on a symmetric capacity region. Recent results by Verloop and Núñez-Queija show that, assuming a single class of flows for each cell, the stochastically optimal dynamic policy is to have both stations switched on whenever there are users in both cells. In this paper, we consider a system where the two stations are able to provide services to two different classes of users - the near ones and the far ones. In this setting, the stochastic optimality of the Both Stations On policy does not necessarily hold, but it may still be a close-to-optimal policy, at least for minimizing the mean flow delay. We present a systematic method based on the policy improvement algorithm of the theory of the Markov Decision Processes to generate a near-optimal state-dependent resource allocation policy. Our numerical experiments with these two dynamic policies indicate that the Both Stations On policy is, indeed, close to optimal even when there are multiple user classes.

Whittle index approach to size-aware scheduling for time-varying channels with multiple states

We consider the optimal opportunistic scheduling problem for downlink data traffic in a wireless cell with time-varying channels. The scheduler itself operates at a very fast time scale of milliseconds, but the objective function is related to minimizing the holding costs at a much longer time scale, at the so-called flow level. The Whittle index approach is a powerful tool in this context, since it renders the flow-level optimization problem with heterogeneous users tractable. Until now, this approach has been applied to the opportunistic scheduling problem to generate non-anticipating index policies that may depend on the amount of attained service but do not utilize the exact size information. In this paper, we produce a size-aware (i.e., anticipating) index policy by applying the Whittle index approach in a novel way. By a numerical study based on simulations, we demonstrate that the resulting size-aware index policy systematically improves performance. As a side result, we show that the opportunistic scheduling problem is indexable when the file sizes follow the Pascal distribution, and we derive the corresponding Whittle index, which generalizes earlier results.

Opportunistic scheduling with flow size information for Markovian time-varying channels

Abstract Opportunistic scheduling refers to algorithms that try to exploit the random variations of the physical layer channel quality in wireless systems for the allocation of radio resources. As indicated by some recent papers, a promising approach to optimize the resource allocation in such a context is to utilize the notion of Whittle index, originally developed for restless multi-armed bandits. In this paper, we apply the Whittle index approach for the opportunistic scheduling problem of downlink data flows assuming two-state Markovian time-varying channels. Until now, this has been done only for geometric flow sizes. Our aim is to allow arbitrary flow size distributions and study how to optimally combine opportunistic scheduling with exact flow size information. We use a phase-type approximation for the flow sizes to make the problem amenable to the Whittle index approach. In the first step, we show that the opportunistic scheduling problem is indexable for Erlang distributed flow sizes and derive the corresponding Whittle index, which generalizes earlier results. In the second step, we utilize these results to develop a size-aware index policy for the original problem. The result is also heuristically generalized to cover Markovian channels with multiple states. By simulation-based numerical studies, we demonstrate that the resulting size-aware index policy is able to appropriately make use of the more exact size information and thus systematically improves performance when compared to earlier developed schedulers.