Work-conserving Scheduling Policies Research Articles

Diffusion parameters of flows in stable multi-class queueing networks

We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes the system stable. We study the variability of flows within the network. Computable expressions for quantifying flow variability have previously been discussed in the literature. However, in this paper, we shed more light on such analysis to justify the use of these expressions in the asymptotic analysis of network flows. Toward that end, we find a simple diffusion limit for the inter-class flows and establish the relation to asymptotic (co-)variance rates.

Optimal Scheduling of Critically Loaded Multiclass GI/M/n+M Queues in an Alternating Renewal Environment

In this paper, we study optimal control problems for multiclass GI/M/n+M queues in an alternating renewal (up-down) random environment in the Halfin-Whitt regime. Assuming that the downtimes are asymptotically negligible and only the service processes are affected, we show that the limits of the diffusion-scaled state processes under non-anticipative, preemptive, work-conserving scheduling policies, are controlled jump diffusions driven by a compound Poisson jump process. We establish the asymptotic optimality of the infinite-horizon discounted and long-run average (ergodic) problems for the queueing dynamics. Since the process counting the number of customers in each class is not Markov, the usual martingale arguments for convergence of mean empirical measures cannot be applied. We surmount this obstacle by demonstrating the convergence of the generators of an augmented Markovian model which incorporates the age processes of the renewal interarrival times and downtimes. We also establish long-run average moment bounds of the diffusion-scaled queueing processes under some (modified) priority scheduling policies. This is accomplished via Foster-Lyapunov equations for the augmented Markovian model.

On Learning the CC Rule: Single and Multi-Server Settings

We consider learning-based variants of the cμ rule -- a classic and well-studied scheduling policy -- in single and multi-server settings for multi-class queueing systems. In the single server setting, the cμ rule is known to minimize the expected holding-cost (weighted queue-lengths summed both over classes and time). We focus on the setting where the service rates μ are unknown, and are interested in the holding-cost regret -- the difference in the expected holding-costs between that induced by a learning-based rule (that learns μ) and that from the cμ rule (which has knowledge of the service rates) over any fixed time horizon. We first show that empirically learning the service rates and then scheduling using these learned values results in a regret of holding-cost that does not depend on the time horizon. The key insight that allows such a constant regret bound is that a work-conserving scheduling policy in this setting allows explore-free learning, where no penalty is incurred for exploring and learning server rates. We next consider the multi-server setting. We show that in general, the cμ rule is not stabilizing (i.e. there are stabilizable arrival and service rate parameters for which the multi-server cμ rule results in unstable queues). We then characterize sufficient conditions for stability (and also concentrations on busy periods). Using these results, we show that learning-based variants of the cμ rule again result in a constant regret (i.e. does not depend on the time horizon). This result hinges on (i) the busy period concentrations of the multi-server cμ rule, and that (ii) our learning-based rule is designed to dynamically explore server rates, but in such a manner that it eventually satisfies an explore-free condition.

Delay-Privacy Tradeoff in the Design of Scheduling Policies

Traditionally, scheduling policies have been optimized to perform well on metrics, such as throughput, delay, and fairness. In the context of shared event schedulers, where a common processor is shared among multiple users, one also has to consider the privacy offered by the scheduling policy. The privacy offered by a scheduling policy measures how much information about the usage pattern of one user of the system can be learned by another as a consequence of sharing the scheduler. We introduced an estimation error-based metric to quantify this privacy. We showed that the most commonly deployed scheduling policy, the first-come-first-served offers very little privacy to its users. We also proposed a parametric nonwork conserving policy, which traded off delay for improved privacy. In this paper, we ask the question, is a tradeoff between delay and privacy fundamental to the design to scheduling policies? In particular, is there a work conserving, possibly randomized, and scheduling policy that scores high on the privacy metric? Answering the first question, we show that there does exist a fundamental limit on the privacy performance of a work-conserving scheduling policy. We quantify this limit. Furthermore, answering the second question, we demonstrate that the round-robin scheduling policy (deterministic policy) is privacy optimal within the class of work-conserving policies.

2014 M&SOM Best Paper Award

I is a pleasure to announce that the 2014 Manufacturing & Service Operations Management Best Paper Award goes to Philipp Afeche for “IncentiveCompatible Revenue Management in Queueing Systems: Optimal Strategic Delay” for its contribution to theory and practice of operations management. The author will receive a $2,000 prize, contributed by the MSOM Society of INFORMS. Each year, all papers published in the journal during the past three years (2011–2013) are eligible for the award, and judging is done through a two-stage process. First, M&SOM Editor Steve Graves and a group of M&SOM associate editors select a small set of finalists from the nominations received. Second, an ad hoc committee, organized by the immediate past president of the MSOM Society, selects the best paper from among the finalists. This year, the ad hoc committee consisted of Charles Corbett, Jeremie Gallien, Amy Ward, and MSOM pastpresident Beril Toktay. They selected the winning paper from a set of five outstanding finalists. The winning paper studies the revenue-maximizing price and lead-time menu and scheduling policy in a queueing system when customers are heterogeneous with respect to their valuations and time sensitivity, and their type is not observable to the firm. A similar problem has been studied from the social optimality perspective. The novelty of this paper stems from the fact that it studies the problem from the point of view of revenue maximization. This makes a fundamental difference. From the social optimality perspective, it makes sense to consider only work-conserving scheduling policies (i.e., the server does not idle in the presence of a queue). This is not the case when the objective is revenue maximization: The firm may want to “strategically delay” the low-priority customers to make sure that the time-sensitive customers choose the high-price, fast-service option. The paper establishes the “strategic delay” concept and develops interesting managerial insights. The following reviewer commentary reflects points made by many of the reviewers:

Bounds on Stability and Latency in Wireless Communication

In this paper, we study stability and latency of routing in wireless networks where it is assumed that no collision will occur. Our approach is inspired by the adversarial queuing theory, which is amended in order to model wireless communication. More precisely, there is an adversary that specifies transmission rates of wireless links and injects data in such a way that an average number of data injected in a single round and routed through a single wireless link is at most r, for a given r ∈ (0, 1). We also assume that the additional "burst" of data injected during any time interval and scheduled via a single link is bounded by a given parameter b. Under this scenario, we show that the nodes following so called work-conserving scheduling policies, not necessarily the same, are guaranteed stability (i.e., bounded queues) and reasonably small data latency (i.e., bounded time on data delivery), for injection rates r <; 1/d, where d is the maximum length of a routing path. Furthermore, we also show that such a bound is asymptotically optimal on d.

Tight Arrival Curve at the Output of a Work-Conserving Blind Multiplexing Server

As a means of supporting quality of service guarantees, aggregate multiplexing has attracted a lot of attention in the networking community, since it requires less complexity than flow-based scheduling. However, contrary to what happens in the case of flow-based multiplexing, few results are available for aggregate-based multiplexing. In this paper, we consider a server multiplexer fed by several flows and analyze the impact caused by traffic aggregation on the flows at the output of the server. No restriction is imposed on the server multiplexer other than the fact that it must operate in a work-conserving fashion. We characterize the best arrival curves that constrain the number of bits that leave the server, in any time interval, for each individual flow. These curves can be used to obtain the delays suffered by packets in complex scenarios where multiplexers are interconnected, as well as to determine the maximum size of the buffers in the different servers. Previous results provide tight delay bounds for networks where servers are of the FIFO type. Here, we provide tight bounds for any work-conserving scheduling policy, so that our results can be applied to heterogeneous networks where the servers (routers) can use different work-conserving scheduling policies such as First-In First-Out (FIFO), Earliest Deadline First (EDF), Strict Priority (SP), Guaranteed Rate scheduling (GR), etc.

Weak instability in stochastic and fluid queueing networks

The fluid model has proven to be one of the most effective tools for the analysis of stochastic queueing networks, specifically for the analysis of stability. It is known that stability of a fluid model implies positive (Harris) recurrence (stability) of a corresponding stochastic queueing network, and weak stability implies rate stability of a corresponding stochastic network. These results have been established both for cases of specific scheduling policies and for the class of all work conserving policies.However, only partial converse results have been established and in certain cases converse statements do not hold. In this paper we close one of the existing gaps. For the case of networks with two stations we prove that if the fluid model is not weakly stable under the class of all work conserving policies, then any corresponding queueing network is not rate stable under the class of all work conserving policies. We establish the result by building a particular work conserving scheduling policy which makes any corresponding stochastic process transient. An important corollary of our result is that the condition of the form ρ* &lt; 1, which was proven in [7) to be the exact condition for global weak stability of the fluid model, is also the exact global rate stability condition for any corresponding queueing network. Here ρ* is a certain computable parameter of the network involving virtual station and push start conditions.

On the Conservation Law and the Performance Space of Single Server Systems

We consider a multiclass GI/G/1 queueing system, operating under an arbitrary work-conserving scheduling policy π. We derive an invariance relation for the Cesaro sums of waiting times under π, which does not require the existence of limits of the Cesaro sums. This allows us to include important classes in the set of admissible policies such as time-dependent and adaptive policies. For these classes of policies, ergodicity is not known a priori and may not even exist. Therefore, the classical invariance relations that involve statistical averages do not hold. For an M/G/1 system, we derive inequalities involving the Cesaro sums of waiting times that further characterize the achievable performance region of the system.