WCFS: a new framework for analyzing multiserver systems (original) (raw)

The Finite-Skip Method for Multiserver Analysis

ArXiv, 2021

Multiserver queueing systems are found at the core of a wide variety of practical systems. Unfortunately, existing tools for analyzing multiserver models have major limitations: Techniques for exact analysis often struggle with high-dimensional models, while techniques for deriving bounds are often too specialized to handle realistic system features, such as variable service rates of jobs. New techniques are needed to handle these complex, important, high-dimensional models. In this paper we introduce the work-conserving finite-skip class of models. This class includes many important models, such as the heterogeneous M/G/k, the limited processor sharing policy for the M/G/1, the threshold parallelism model, and the multiserver-job model under a simple scheduling policy. We prove upper and lower bounds on mean response time for any model in the work-conserving finite-skip class. Our bounds are separated by an additive constant, giving a strong characterization of mean response time a...

Optimal Scheduling in the Multiserver-job Model under Heavy Traffic

Proceedings of the ACM on Measurement and Analysis of Computing Systems

Multiserver-job systems, where jobs require concurrent service at many servers, occur widely in practice. Essentially all of the theoretical work on multiserver-job systems focuses on maximizing utilization, with almost nothing known about mean response time. In simpler settings, such as various known-size single-server-job settings, minimizing mean response time is merely a matter of prioritizing small jobs. However, for the multiserver-job system, prioritizing small jobs is not enough, because we must also ensure servers are not unnecessarily left idle. Thus, minimizing mean response time requires prioritizing small jobs while simultaneously maximizing throughput. Our question is how to achieve these joint objectives. We devise the ServerFilling-SRPT scheduling policy, which is the first policy to minimize mean response time in the multiserver-job model in the heavy traffic limit. In addition to proving this heavy-traffic result, we present empirical evidence that ServerFilling-SR...

Approximations in performance analysis of a controllable queueing system with heterogeneous servers

Mathematics, 2020

The paper studies a controllable multi-server heterogeneous queueing system where servers 1 operate at different service rates without preemption, i.e. the service times are uninterrupted. The 2 optimal control policy allocates the customers between the servers in such a way that the mean 3 number of customers in the system reaches its minimal value. The Markov decision model and the 4 policy-iteration algorithm are used to calculate the optimal allocation policy and corresponding mean 5 performance characteristics. The optimal policy, when neglecting the weak influence of slow servers, 6 is of threshold type defined as a sequence of threshold levels which specifies the queue lengths 7 for the usage of any slower server. To avoid time-consuming calculations for systems with a large 8 number of servers, we focus here on a heuristic evaluation of the optimal thresholds and compare this 9 solution with the real values. We develop also the simple lower and upper bound methods based on 10 approximation by an equivalent heterogeneous queueing system with a preemption to measure the 11 mean number of customers in the system operating under the optimal policy. Finally, the simulation 12 technique is used to provide sensitivity analysis of the heuristic solution to changes in the form of 13 inter-arrival and service time distributions. 14 Keywords: Heterogeneous servers; Markov decision process; policy-iteration algorithm; mean 15 number of customers; decomposable semi-regenerative process 16