Alexander L. Stolyar

Providing quality of service over a shared wireless link

We propose an efficient way to support quality of service of multiple real-time data users sharing a wireless channel. We show how scheduling algorithms exploiting asynchronous variations of channel quality can be used to maximize the channel capacity (i.e., maximize the number of users that can be supported with the desired QoS).

Maximizing Queueing Network Utility Subject to Stability: Greedy Primal-Dual Algorithm

We study a model of controlled queueing network, which operates and makes control decisions in discrete time. An underlying random network mode determines the set of available controls in each time slot. Each control decision “produces” a certain vector of “commodities”; it also has associated “traditional” queueing control effect, i.e., it determines traffic (customer) arrival rates, service rates at the nodes, and random routing of processed customers among the nodes. The problem is to find a dynamic control strategy which maximizes a concave utility function H(X), where X is the average value of commodity vector, subject to the constraint that network queues remain stable.We introduce a dynamic control algorithm, which we call Greedy Primal-Dual (GPD) algorithm, and prove its asymptotic optimality. We show that our network model and GPD algorithm accommodate a wide range of applications. As one example, we consider the problem of congestion control of networks where both traffic sources and network processing nodes may be randomly time-varying and interdependent. We also discuss a variety of resource allocation problems in wireless networks, which in particular involve average power consumption constraints and/or optimization, as well as traffic rate constraints.

Scheduling algorithms for a mixture of real-time and non-real-time data in HDR

High Data Rate (HDR) technology has recently been proposed as an overlay to CDMA as a means of providing packet data service to mobile users. In this paper, we study various scheduling algorithms for a mixture of real-time and non-real-time data over HDR/CDMA and compare their performance. We study the performance with respect to packet delays and also average throughput, where we use a token based mechanism to give minimum throughput guarantees. We find that a rule which we call the exponential rule performs well with regard to both these criteria. (In a companion paper, we show that this rule is throughput-optimal, i.e., it makes the queues stable if it is feasible to do so with any other scheduling rule). Our main conclusion is that intelligent scheduling algorithms in conjunction with token based rate control provide an efficient framework for supporting a mixture of real-time and non-real-time data applications in a single carrier.

SCHEDULING IN A QUEUING SYSTEM WITH ASYNCHRONOUSLY VARYING SERVICE RATES

We consider the following queuing system which arises as a model of a wireless link shared by multiple users. There is a finite number N of input flows served by a server. The system operates in discrete time t = 0,1,2,…. Each input flow can be described as an irreducible countable Markov chain; waiting customers of each flow are placed in a queue. The sequence of server states m(t), t = 0,1,2,…, is a Markov chain with finite number of states M. When the server is in state m, it can serve mim customers of flow i (in one time slot).The scheduling discipline is a rule that in each time slot chooses the flow to serve based on the server state and the state of the queues. Our main result is that a simple online scheduling discipline, Modified Largest Weighted Delay First, along with its generalizations, is throughput optimal; namely, it ensures that the queues are stable as long as the vector of average arrival rates is within the system maximum stability region.

On the Asymptotic Optimality of the Gradient Scheduling Algorithm for Multiuser Throughput Allocation

We consider the model whereN queues (users) are served in discrete time by a generalized switch. The switch state is random, and it determines the set of possible service rate choices (scheduling decisions) in each time slot. This model is primarily motivated by the problem of scheduling transmissions ofN data users in a shared time-varying wireless environment, but also includes other applications such as input-queued cross-bar switches and parallel flexible server systems.The objective is to find a scheduling strategy maximizing a concave utility functionH( u1,..., uN ), whereu n s are long-term average service rates (data throughputs) of the users, assuming users always have data to be served.We prove asymptotic optimality of the gradient scheduling algorithm (which generalizes the well-known proportional fair algorithm) for our model, which, in particular, allows for simultaneous service of multiple users and for discrete sets of scheduling decisions. Analysis of the transient dynamics of user throughputs is the key part of this work.

Optimal utility based multi-user throughput allocation subject to throughput constraints

We consider the problem of scheduling multiple users sharing a time-varying wireless channel. (As an example, this is a model of scheduling in 3G wireless technologies, such as CDMA2000 3G1xEV-DO downlink scheduling.) We introduce an algorithm which seeks to optimize a concave utility function /spl Sigma//sub i/H/sub i/(R/sub i/) of the user throughputs R/sub i/, subject to certain lower and upper throughput bounds: R/sub i//sup min//spl les/R/sub i//spl les/R/sub i//sup max/. The algorithm, which we call the gradient algorithm with minimum/maximum rate constraints (GMR) uses a token counter mechanism, which modifies an algorithm solving the corresponding unconstrained problem, to produce the algorithm solving the problem with throughput constraints. Two important special cases of the utility functions are /spl Sigma//sub i/log R/sub i/ and /spl Sigma//sub i/R/sub i/, corresponding to the common proportional fairness and throughput maximization objectives. We study the dynamics of user throughputs under GMR algorithm, and show that GMR is asymptotically optimal in the following sense. If, under an appropriate scaling, the throughput vector R(t) converges to a fixed vector R/sup +/ as time t/spl rarr//spl infin/ then R/sup +/ is an optimal solution to the optimization problem described above. We also present simulation results showing the algorithm performance.

Novel Architectures and Algorithms for Delay Reduction in Back-Pressure Scheduling and Routing

The back-pressure algorithm is a well-known throughput-optimal algorithm. However, its delay performance may be quite poor even when the traffic load is not close to network capacity due to the following two reasons. First, each node has to maintain a separate queue for each commodity in the network, and only one queue is served at a time. Second, the backpressure routing algorithm may route some packets along very long routes. In this paper, we present solutions to address both of the above issues, and hence, improve the delay performance of the back-pressure algorithm. One of the suggested solutions also decreases the complexity of the queueing data structures to be maintained at each node.

Joint Scheduling and Congestion Control in Mobile Ad-Hoc Networks

In this paper we study the problem of jointly performing scheduling and congestion control in mobile ad-hoc networks so that network queues remain bounded and the resulting flow rates satisfy an associated network utility maximization problem. In recent years a number of papers have presented theoretical solutions to this problem that are based on combining differential-backlog scheduling algorithms with utility-based congestion control. However, this work typically does not address a number of issues such as how signaling should be performed and how the new algorithms interact with other wireless protocols. In this paper we address such issues. In particular: ldr We define a specific network utility maximization problem that we believe is appropriate for mobile adhoc networks. ldr We describe a wireless greedy primal dual (wGPD) algorithm for combined congestion control and scheduling that aims to solve this problem. ldr We show how the wGPD algorithm and its associated signaling can be implemented in practice with minimal disruption to existing wireless protocols. ldr We show via OPNET simulation that wGPD significantly outperforms standard protocols such as 802.11 operating in conjunction with TCP. This work was supported by the DARPA CBMANET program.

Pathwise optimality of the exponential scheduling rule for wireless channels

We consider the problem of scheduling the transmissions of multiple data users (flows) sharing the same wireless channel (server). The unique feature of this problem is the fact that the capacity (service rate) of the channel varies randomly with time and asynchronously for different users. We study a scheduling policy called the exponential scheduling rule, which was introduced in an earlier paper. Given a system with N users, and any set of positive numbers {a n }, n = 1, 2,…, N, we show that in a heavy-traffic limit, under a nonrestrictive ‘complete resource pooling’ condition, this algorithm has the property that, for each time t, it (asymptotically) minimizes max n a n q̃ n (t), where q̃ n (t) is the queue length of user n in the heavy-traffic regime.

A novel architecture for reduction of delay and queueing structure complexity in the back-pressure algorithm

The back-pressure algorithm is a well-known throughput-optimal algorithm. However, its implementation requires that each node has to maintain a separate queue for each commodity in the network, and only one queue is served at a time. This fact may lead to a poor delay performance even when the traffic load is not close to network capacity. Also, since the number of commodities in the network is usually very large, the queueing data structure that has to be maintained at each node is respectively complex. In this paper, we present a solution to address both of these issues in the case of a fixed-routing network scenario where the route of each flow is chosen upon arrival. Our proposed architecture allows each node to maintain only per-neighbor queues and, moreover, improves the delay performance of the back-pressure algorithm.