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.
We consider the stability of robust scheduling policies for multiclass queueing networks. These are open networks with arbitrary routing matrix and several disjoint groups of queues in which at most one queue can be served at a time. The arrival and potential service processes and routing decisions at the queues are independent, stationary and ergodic. A scheduling policy is called robust if it does not depend on the arrival and service rates nor on the routing probabilities. A policy is called throughput-optimal if it makes the system stable whenever the parameters are such that the system ca…
We consider the problem of packet scheduling in single-hop queueing networks, 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…
We consider a server serving a time-slotted queued system of multiple packet-based flows, with exogenous packet arrivals and time-varying service rates. At each time, the server can observe instantaneous service rates for only a subset of flows (from within a fixed collection of observable subsets) before scheduling a flow in the subset for service. We are interested in queue-length aware scheduling to keep the queues short, and develop scheduling algorithms that use only partial service rate information from subsets of channels to minimize the likelihood of queue overflow in the system. Speci…
In the study of large scale stochastic networks with resource management, differential equations and mean-field limits are two key techniques. Recent research shows that the expected fraction vector (that is, the tailed probability vector) plays a key role in setting up mean-field differential equations. To further apply the technique of tailed probability vector to deal with resource management of large scale stochastic networks, this paper discusses tailed probabilities in some basic queueing processes including QBD processes, Markov chains of GI/M/1 type and of M/G/1 type, and also provides…
We consider a set of transmitter-receiver pairs, or links, that share a common channel and address the problem of emptying backlogged queues at the transmitters in minimum time. The problem amounts to determining activation subsets of links and their time durations to form a minimum-length schedule. The problem of scheduling has been studied under various formulations before. In this paper, we present fundamental insights and solution characterizations that include: (i) showing that the complexity of the problem remains high for any continuous and increasing rate function, (ii) formulating and…
We analyze opportunistic schemes for transmission scheduling from one of $n$ homogeneous queues whose channel states fluctuate independently. Considered schemes consist of the LCQ policy, which transmits from a longest connected queue in the entire system, and its low-complexity variants that transmit from a longest queue within a randomly chosen subset of connected queues. A Markovian model is studied where mean packet transmission time is $n^{-1}$ and packet arrival rate is $λ<1$ per queue. Transient and equilibrium distributions of queue occupancies are obtained in the limit as the system s…
We investigate the performance of First-In, First-Out (FIFO) queues over wireless networks. We characterize the stability region of a general scenario where an arbitrary number of FIFO queues, which are served by a wireless medium, are shared by an arbitrary number of flows. In general, the stability region of this system is non-convex. Thus, we develop a convex inner-bound on the stability region, which is provably tight in certain cases. The convexity of the inner bound allows us to develop a resource allocation scheme; dFC. Based on the structure of dFC, we develop a stochastic flow control…
Motivated by medium access control for resource-challenged wireless Internet of Things (IoT), we consider the problem of queue scheduling with reduced queue state information. In particular, we consider a time-slotted scheduling model with $N$ sensor nodes, with pair-wise dependence, such that Nodes $i$ and $i + 1,~0 < i < N$ cannot transmit together. We develop new throughput-optimal scheduling policies requiring only the empty-nonempty state of each queue that we term Queue Nonemptiness-Based (QNB) policies. We propose a Policy Splicing technique to combine scheduling policies for small netw…
In this paper we consider greedy scheduling algorithms in wireless networks, i.e., the schedules are computed by adding links greedily based on some priority vector. Two special cases are considered: 1) Longest Queue First (LQF) scheduling, where the priorities are computed using queue lengths, and 2) Static Priority (SP) scheduling, where the priorities are pre-assigned. We first propose a closed-form lower bound stability region for LQF scheduling, and discuss the tightness result in some scenarios. We then propose an lower bound stability region for SP scheduling with multiple priority vect…
In this paper, we consider a queueing system with multiple channels (or servers) and multiple classes of users. We aim at allocating the available channels among the users in such a way to minimize the expected total average queue length of the system. This known scheduling problem falls in the framework of Restless Bandit Problems (RBP) for which an optimal solution is known to be out of reach for the general case. The contributions of this paper are as follows. We rely on the Lagrangian relaxation method to characterize the Whittle index values and to develop an index-based heuristic for the…
In this paper, we investigate a general delay-aware channel allocation problem where the number of channels is less than that of users. Due to the proliferation of delay sensitive applications, the objective of our problem is chosen to be the minimization of the total average backlog queues of the network in question. First, we show that our problem falls in the framework of Restless Bandit Problems (RBP), for which obtaining the optimal solution is known to be out of reach. To circumvent this difficulty, we tackle the problem by adopting a Whittle index approach. To that extent, we employ a L…
A coflow is a collection of parallel flows belonging to the same job. It has the all-or-nothing property: a coflow is not complete until the completion of all its constituent flows. In this paper, we focus on optimizing \emph{coflow-level delay}, i.e., the time to complete all the flows in a coflow, in the context of an $N\times N$ input-queued switch. In particular, we develop a throughput-optimal scheduling policy that achieves the best scaling of coflow-level delay as $N\rightarrow\infty$. We first derive lower bounds on the coflow-level delay that can be achieved by any scheduling policy. …
We study the scheduling polices for asymptotically optimal delay in queueing systems with switching overhead. Such systems consist of a single server that serves multiple queues, and some capacity is lost whenever the server switches to serve a different set of queues. The capacity loss due to this switching overhead can be significant in many emerging applications, and needs to be explicitly addressed in the design of scheduling policies. For example, in 60GHz wireless networks with directional antennas, base stations need to train and reconfigure their beam patterns whenever they switch from…
We consider a switched (queuing) network in which there are constraints on which queues may be served simultaneously; such networks have been used to effectively model input-queued switches and wireless networks. The scheduling policy for such a network specifies which queues to serve at any point in time, based on the current state or past history of the system. In the main result of this paper, we provide a new class of online scheduling policies that achieve optimal queue-size scaling for a class of switched networks including input-queued switches. In particular, it establishes the validit…
Scheduling and managing queues with bounded buffers are among the most fundamental problems in computer networking. Traditionally, it is often assumed that all the properties of each packet are known immediately upon arrival. However, as traffic becomes increasingly heterogeneous and complex, such assumptions are in many cases invalid. In particular, in various scenarios information about packet characteristics becomes available only after the packet has undergone some initial processing. In this work, we study the problem of managing queues with limited knowledge. We start by showing lower bo…
Stability with respect to a given scheduling policy has become an important issue for wireless communication systems, but it is hard to prove in particular scenarios. In this paper two simple conditions for stability in broadcast channels are derived, which are easy to check. Heuristically, the conditions imply that if the queue length in the system becomes large, the rate allocation is always the solution of a weighted sum rate maximization problem. Furthermore, the change of the weight factors between two time slots becomes smaller and the weight factors of the users, whose queues are bounde…
We consider a dynamic server control problem for two parallel queues with randomly varying connectivity and server switchover time between the queues. At each time slot the server decides either to stay with the current queue or switch to the other queue based on the current connectivity and the queue length information. The introduction of switchover time is a new modeling component of this problem, which makes the problem much more challenging. We develop a novel approach to characterize the stability region of the system by using state action frequencies, which are stationary solutions to a…
Flow scheduling is crucial in data centers, as it directly influences user experience of applications. According to different assumptions and design goals, there are four typical flow scheduling problems/solutions: SRPT, LAS, Fair Queueing, and Deadline-Aware scheduling. When implementing these solutions in commodity switches with limited number of queues, they need to set static parameters by measuring traffic in advance, while optimal parameters vary across time and space. This paper proposes a generic framework, namely QCluster, to adapt all scheduling problems for limited number of queues.…
Low latency is highly desirable for cloud services. To achieve low response time, stringent timing requirements are needed for task scheduling in a large-scale server farm spanning thousands of servers. In this paper, we conduct an in-depth analysis for distributed Join-the-Idle-Queue (JIQ), a promising new approximation of an idealized task-scheduling algorithm. In particular, we derive semi-closed form expressions for the delay performance of distributed JIQ, and we propose a new variant of distributed JIQ that offers clear advantages over alternative algorithms for large systems.
In this paper, we study the stability of light traffic achieved by a scheduling algorithm which is suitable for heterogeneous traffic networks. Since analyzing a scheduling algorithm is intractable using the conventional mathematical tool, our goal is to minimize the largest queue-overflow probability achieved by the algorithm. In the large deviation setting, this problem is equivalent to maximizing the asymptotic decay rate of the largest queue-overflow probability. We first derive an upper bound on the decay rate of the queue overflow probability as the queue overflow threshold approaches in…
Age of information (AoI) is a recently proposed metric that measures the time elapsed since the generation of the last received information update. We consider the problem of AoI minimization for a network under general interference constraints, and time varying channel. We study the case where the channel statistics are known, but the current channel state is unknown. We propose two scheduling policies, namely, the virtual queue based policy and age-based policy. In the virtual queue based policy, the scheduler schedules links with maximum weighted sum of the virtual queue lengths, while in t…
Throughput-optimal transmission scheduling in wireless networks has been a well considered problem in the literature, and the method for achieving optimality, MaxWeight scheduling, has been known for several decades. This algorithm achieves optimality by adaptively scheduling transmissions relative to each user's stochastic traffic demands. To implement the method, users must report their queue backlogs to the network controller and must rapidly respond to the resulting resource allocations. However, many currently-deployed wireless systems are not able to perform these tasks and instead expec…
For wireless caching networks, the scheme design for content delivery is non-trivial in the face of the following tradeoff. On one hand, to optimize overall throughput, users can associate their nearby APs with great channel capacities; however, this may lead to unstable queue backlogs on APs and prolong request delays. On the other hand, to ensure queue stability, some users may have to associate APs with inferior channel states, which would incur throughput loss. Moreover, for such systems, how to conduct predictive scheduling to reduce delays and the fundamental limits of its benefits remai…
We investigate the downlink scheduling problem under Markovian ON/OFF fading channels, where the instantaneous channel state information is not directly accessible, but is revealed via ARQ-type feedback. The scheduler can exploit the temporal correlation/channel memory inherent in the Markovian channels to improve network performance. However, designing low-complexity and throughput-optimal algorithms under temporal correlation is a challenging problem. In this paper, we find that under an average number of transmissions constraint, a low-complexity index policy is throughput-optimal. The poli…
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 back-pressure 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 …
Scheduling is a critical and challenging resource allocation mechanism for multihop wireless networks. It is well known that scheduling schemes that favor links with larger queue length can achieve high throughput performance. However, these queue-length-based schemes could potentially suffer from large (even infinite) packet delays due to the well-known last packet problem, whereby packets belonging to some flows may be excessively delayed due to lack of subsequent packet arrivals. Delay-based schemes have the potential to resolve this last packet problem by scheduling the link based on the d…
Internet performance is tightly related to the properties of TCP and UDP protocols, jointly responsible for the delivery of the great majority of Internet traffic. It is well understood how these protocols behave under FIFO queuing and what the network congestion effects. However, no comprehensive analysis is available when flow-aware mechanisms such as per-flow scheduling and dropping policies are deployed. Previous simulation and experimental results leave a number of unanswered questions. In the paper, we tackle this issue by modeling via a set of fluid non-linear ODEs the instantaneous thr…
Utilizing customers' service-time information, we study an easy-to-implement scheduling policy with two priority classes. By carefully designing the classes, the two-class priority rule achieves near-optimal performance. In particular, for a single-server queue, as the traffic intensity approaches 1, the policy achieves a scaling for the queue length processes that is similar to the shortest remaining processing time first policy. Our analysis quantifies how the tail of the service time distribution affects the benefits one can gain from service-time-based scheduling policies. When the service…
We study the conditional sojourn time distributions of processor sharing (PS), foreground background processor sharing (FBPS) and shortest remaining processing time first (SRPT) scheduling disciplines on an event where the job size of a customer arriving in stationarity is smaller than exactly k>=0 out of the preceding m>=k arrivals. Then, conditioning on the preceding event, the sojourn time distribution of this newly arriving customer behaves asymptotically the same as if the customer were served in isolation with a server of rate (1-ρ)/(k+1) for PS/FBPS, and (1-ρ) for SRPT, respectively, wh…
It is by now well-known that wireless networks with file arrivals and departures are stable if one uses alpha-fair congestion control and back-pressure based scheduling and routing. In this paper, we examine whether ?alpha-fair congestion control is necessary for flow-level stability. We show that stability can be ensured even with very simple congestion control mechanisms, such as a fixed window size scheme which limits the maximum number of packets that are allowed into the ingress queue of a flow. A key ingredient of our result is the use of the difference between the logarithms of queue le…
In this paper we consider a real time queuing system with rewards and deadlines. We assume that packet processing time is known upon arrival, as is the case in communication networks. This assumption allows us to demonstrate that the well known Earliest-Deadline-First policy performance can be improved. We then propose a scheduling policy that provides excellent results for packets with rewards and deadlines. We prove that the policy is optimal under deterministic service time and binomial reward distribution. In the more general case we prove that the policy processes the maximal number of pa…
In this paper, we study the delay-constrained input-queued switch where each packet has a deadline and it will expire if it is not delivered before its deadline. Such new scenario is motivated by the proliferation of real-time applications in multimedia communication systems, tactile Internet, networked controlled systems, and cyber-physical systems. The delay-constrained input-queued switch is completely different from the well-understood delay-unconstrained one and thus poses new challenges. We focus on three fundamental problems centering around the performance metric of timely throughput: …
Network Utility Maximization (NUM) studies the problems of allocating traffic rates to network users in order to maximize the users' total utility subject to network resource constraints. In this paper, we propose a new NUM framework, Learning-NUM, where the users' utility functions are unknown apriori and the utility function values of the traffic rates can be observed only after the corresponding traffic is delivered to the destination, which means that the utility feedback experiences \textit{queueing delay}. The goal is to design a policy that gradually learns the utility functions and mak…
We consider the problem of distributed scheduling in wireless networks where heterogeneously delayed information about queue lengths and channel states of all links are available at all the transmitters. In an earlier work (by Reddy et al. in Queueing Systems, 2012), a throughput optimal scheduling policy (which we refer to henceforth as the R policy) for this setting was proposed. We study the R policy, and examine its two drawbacks -- (i) its huge computational complexity, and (ii) its non-optimal average per-packet queueing delay. We show that the R policy unnecessarily constrains itself to…
We study auction-theoretic scheduling in cellular networks using the idea of mean field equilibrium (MFE). Here, agents model their opponents through a distribution over their action spaces and play the best response. The system is at an MFE if this action is itself a sample drawn from the assumed distribution. In our setting, the agents are smart phone apps that generate service requests, experience waiting costs, and bid for service from base stations. We show that if we conduct a second-price auction at each base station, there exists an MFE that would schedule the app with the longest queu…
Interactive applications with automated feedback will largely influence the design of future networked infrastructures. In such applications, status information about an environment of interest is captured and forwarded to a compute node, which analyzes the information and generates a feedback message. Timely processing and forwarding must ensure the feedback information to be still applicable; thus, the quality-of-service parameter for such applications is the end-to-end latency over the entire loop. By modelling the communication of a feedback loop as a two-hop network, we address the proble…
Datacenters are the main infrastructure on top of which cloud computing services are offered. Such infrastructure may be shared by a large number of tenants and applications generating a spectrum of datacenter traffic. Delay sensitive applications and applications with specific Service Level Agreements (SLAs), generate deadline constrained flows, while other applications initiate flows that are desired to be delivered as early as possible. As a result, datacenter traffic is a mix of two types of flows: deadline and regular. There are several scheduling policies for either traffic type with foc…
