Queue Length Asymptotics for Generalized Max-Weight Scheduling in the presence of Heavy-Tailed Traffic

We investigate the asymptotic behavior of the steady-state queue length distribution under generalized max-weight scheduling in the presence of heavy-tailed traffic. We consider a system consisting of two parallel queues, served by a single server. One of the queues receives heavy-tailed traffic, and the other receives light-tailed traffic. We study the class of throughput optimal max-weight-alpha scheduling policies, and derive an exact asymptotic characterization of the steady-state queue length distributions. In particular, we show that the tail of the light queue distribution is heavier than a power-law curve, whose tail coefficient we obtain explicitly. Our asymptotic characterization also contains an intuitively surprising result - the celebrated max-weight scheduling policy leads to the worst possible tail of the light queue distribution, among all non-idling policies. Motivated by the above negative result regarding the max-weight-alpha policy, we analyze a log-max-weight (LMW) scheduling policy. We show that the LMW policy guarantees an exponentially decaying light queue tail, while still being throughput optimal

Scheduling strategies to mitigate the impact of bursty traffic in wireless networks

Recent work has shown that certain queue-length based scheduling algorithms, such as max-weight, can lead to poor delays in the presence of bursty traffic. To overcome this phenomenon, we consider the problem of designing scheduling policies that are robust to bursty traffic, while also amenable to practical implementation. Specifically, we discuss two mechanisms, one based on adaptive CSMA, and the second based on maximum-weight scheduling with capped queue lengths. We consider a simple queueing network consisting of two conflicting links. The traffic served by the first link is bursty, and is modeled as being heavy-tailed, while traffic at the second link is modeled using a light-tailed arrival process. In this setting, previous work has shown that even the light-tailed traffic would experience heavy-tailed delays under max-weight scheduling. In contrast, we demonstrate a threshold phenomenon in the relationship between the arrival rates and the queue backlog distributions. In particular, we show that with an adaptive CSMA scheme, when the arrival rate of the light-tailed traffic is less than a threshold value, the light-tailed traffic experiences a light-tailed queue backlog at steady state, whereas for arrival rates above the same threshold, the light-tailed traffic experiences a heavy-tailed queue backlog. We also show that a similar threshold behavior for max-weight scheduling with capped queue lengthsNational Science Foundation (U.S.) (Grant CNS-0915988)National Science Foundation (U.S.) (Grant CNS-1217048)United States. Army Research Office. Multidisciplinary University Research Initiative (Grant W911NF-08-1-0238

Max-weight scheduling in networks with heavy-tailed traffic

We consider the problem of packet scheduling in a single-hop network with a mix of heavy-tailed and light-tailed traffic, and analyze the impact of heavy-tailed traffic on the performance of Max-Weight scheduling. As a performance metric we use the delay stability of traffic flows: a traffic flow is delay stable if its expected steady-state delay is finite, and delay unstable otherwise. First, we show that a heavy-tailed traffic flow is delay unstable under any scheduling policy. Then, we focus on the celebrated Max-Weight scheduling policy, and show that a light-tailed flow that conflicts with a heavy-tailed flow is also delay unstable. This is true irrespective of the rate or the tail distribution of the light-tailed flow, or other scheduling constraints in the network. Surprisingly, we show that a light-tailed flow can be delay unstable, even when it does not conflict with heavy-tailed traffic. Furthermore, delay stability in this case may depend on the rate of the light-tailed flow. Finally, we turn our attention to the class of Max-Weight-α scheduling policies; we show that if the α-parameters are chosen suitably, then the sum of the α-moments of the steady-state queue lengths is finite. We provide an explicit upper bound for the latter quantity, from which we derive results related to the delay stability of traffic flows, and the scaling of moments of steady-state queue lengths with traffic intensity

Throughput Optimal Scheduling Over Time-Varying Channels in the Presence of Heavy-Tailed Traffic

We study the problem of scheduling over time varying links in a network that serves both heavy-tailed and light tailed traffic. We consider a system consisting of two parallel queues, served by a single server. One of the queues receives heavy-tailed traffic (the heavy queue), and the other receives light-tailed traffic (the light queue). The queues are connected to the server through time-varying ON/OFF links, which model fading wireless channels. We first show that the policy that gives complete priority to the light-tailed traffic guarantees the best possible tail behavior of both queue backlog distributions, whenever the queues are stable. However, the priority policy is not throughput maximizing, and can cause undesirable instability effects in the heavy queue. Next, we study the class of throughput optimal max-weight-α scheduling policies. We discover a threshold phenomenon, and show that the steady state light queue backlog distribution is heavy-tailed for arrival rates above a threshold value, and light-tailed otherwise. We also obtain the exact tail coefficient of the light queue backlog distribution under max-weight-α scheduling. Finally, we study a log-max-weight scheduling policy, which is throughput optimal, and ensures that the light queue backlog distribution is light-tailed.National Science Foundation (U.S.) (Grant CNS-1217048)National Science Foundation (U.S.) (Grant CNS-0915988)National Science Foundation (U.S.) (CMMI-1234062)United States. Army Research Office. Multidisciplinary University Research Initiative (Grant W911NF-08-1-0238

Max-Weight Scheduling in Queueing Networks With Heavy-Tailed Traffic

We consider the problem of scheduling in a single-hop switched network with a mix of heavy-tailed and light-tailed traffic and analyze the impact of heavy-tailed traffic on the performance of Max-Weight scheduling. As a performance metric, we use the delay stability of traffic flows: A traffic flow is delay-stable if its expected steady-state delay is finite, and delay-unstable otherwise. First, we show that a heavy-tailed traffic flow is delay-unstable under any scheduling policy. Then, we focus on the celebrated Max-Weight scheduling policy and show that a light-tailed flow that conflicts with a heavy-tailed flow is also delay-unstable. This is true irrespective of the rate or the tail distribution of the light-tailed flow or other scheduling constraints in the network. Surprisingly, we show that a light-tailed flow can become delay-unstable, even when it does not conflict with heavy-tailed traffic. Delay stability in this case may depend on the rate of the light-tailed flow. Finally, we turn our attention to the class of Max-Weight-α scheduling policies. We show that if the α-parameters are chosen suitably, then the sum of the α-moments of the steady-state queue lengths is finite. We provide an explicit upper bound for the latter quantity, from which we derive results related to the delay stability of traffic flows, and the scaling of moments of steady-state queue lengths with traffic intensity.National Science Foundation (U.S.) (Grant CNS-0915988)National Science Foundation (U.S.) (Grant CCF-0728554)United States. Air Force. Office of Scientific Research. Multidisciplinary University Research Initiative (Grant W911NF-08- 1-0238

Asymptotic performance of queue length based network control policies

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 199-204).In a communication network, asymptotic quality of service metrics specify the probability that the delay or buffer occupancy becomes large. An understanding of these metrics is essential for providing worst-case delay guarantees, provisioning buffer sizes in networks, and to estimate the frequency of packet-drops due to buffer overflow. Second, many network control tasks utilize queue length information to perform effectively, which inevitably adds to the control overheads in a network. Therefore, it is important to understand the role played by queue length information in network control, and its impact on various performance metrics. In this thesis, we study the interplay between the asymptotic behavior of buffer occupancy, queue length information, and traffic statistics in the context of scheduling, flow control, and resource allocation. First, we consider a single-server queue and deal with the question of how often control messages need to be sent in order to effectively control congestion in the queue. Our results show that arbitrarily infrequent queue length information is sufficient to ensure optimal asymptotic decay for the congestion probability, as long as the control information is accurately received. However, if the control messages are subject to errors, the congestion probability can increase drastically, even if the control messages are transmitted often. Next, we consider a system of parallel queues sharing a server, and fed by a statistically homogeneous traffic pattern. We obtain the large deviation exponent of the buffer overflow probability under the well known max-weight scheduling policy. We also show that the queue length based max-weight scheduling outperforms some well known queue-blind policies in terms of the buffer overflow probability. Finally, we study the asymptotic behavior of the queue length distributions when a mix of heavy-tailed and light-tailed traffic flows feeds a system of parallel queues. We obtain an exact asymptotic queue length characterization under generalized max-weight scheduling. In contrast to the statistically homogeneous traffic scenario, we show that max-weight scheduling leads to poor asymptotic behavior for the light-tailed traffic, whereas a queue-blind priority policy gives good asymptotic behavior.by Krishna Prasanna Jagannathan.Ph.D

Modeling, analysis, and optimization for wireless networks in the presence of heavy tails

The heavy-tailed traffic from wireless users, caused by the emerging Internet and multimedia applications, induces extremely dynamic and variable network environment, which can fundamentally change the way in which wireless networks are conceived, designed, and operated. This thesis is concerned with modeling, analysis, and optimization of wireless networks in the presence of heavy tails. First, a novel traffic model is proposed, which captures the inherent relationship between the traffic dynamics and the joint effects of the mobility variability of network users and the spatial correlation in their observed physical phenomenon. Next, the asymptotic delay distribution of wireless users is analyzed under different traffic patterns and spectrum conditions, which reveals the critical conditions under which wireless users can experience heavy-tailed delay with significantly degraded QoS performance. Based on the delay analysis, the fundamental impact of heavy-tailed environment on network stability is studied. Specifically, a new network stability criterion, namely moment stability, is introduced to better characterize the QoS performance in the heavy-tailed environment. Accordingly, a throughput-optimal scheduling algorithm is proposed to maximize network throughput while guaranteeing moment stability. Furthermore, the impact of heavy-tailed spectrum on network connectivity is investigated. Towards this, the necessary conditions on the existence of delay-bounded connectivity are derived. To enhance network connectivity, the mobility-assisted data forwarding scheme is exploited, whose important design parameters, such as critical mobility radius, are derived. Moreover, the latency in wireless mobile networks is analyzed, which exhibits asymptotic linearity in the initial distance between mobile users.Ph.D

Concave Switching in Single and Multihop Networks

Switched queueing networks model wireless networks, input queued switches and numerous other networked communications systems. For single-hop networks, we consider a {($\alpha,g$)-switch policy} which combines the MaxWeight policies with bandwidth sharing networks -- a further well studied model of Internet congestion. We prove the maximum stability property for this class of randomized policies. Thus these policies have the same first order behavior as the MaxWeight policies. However, for multihop networks some of these generalized polices address a number of critical weakness of the MaxWeight/BackPressure policies. For multihop networks with fixed routing, we consider the Proportional Scheduler (or (1,log)-policy). In this setting, the BackPressure policy is maximum stable, but must maintain a queue for every route-destination, which typically grows rapidly with a network's size. However, this proportionally fair policy only needs to maintain a queue for each outgoing link, which is typically bounded in number. As is common with Internet routing, by maintaining per-link queueing each node only needs to know the next hop for each packet and not its entire route. Further, in contrast to BackPressure, the Proportional Scheduler does not compare downstream queue lengths to determine weights, only local link information is required. This leads to greater potential for decomposed implementations of the policy. Through a reduction argument and an entropy argument, we demonstrate that, whilst maintaining substantially less queueing overhead, the Proportional Scheduler achieves maximum throughput stability.Comment: 28 page