Stationary analysis of the "Shortest Queue First" service policy: The asymmetric case. Issue 2 (3rd April 2017)

• Record Type: Journal Article
• Authors: Guillemin, Fabrice; Simonian, Alain
• Is Part Of: Stochastic models. Volume 33:Issue 2(2017)
• Page Start: 256
• Page End: 296
• Publication Date: 2017-04-03
• Subjects: Functional equations in the complex plane -- Markov processes on continuous state spaces -- performance evaluation and queuing -- stochastic scheduling theory; 60J25 -- 30D05 -- 68M20 -- 90B36; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/15326349.2016.1269291
• Languages: English
• ISSNs: 1532-6349

Abstract

ABSTRACT: The Shortest Queue First service discipline is analyzed for two asymmetric queues. For Poisson job arrivals and exponentially distributed service times, we first show that the Laplace transform of workloads in each queue is related to the solutionM of a two-dimensional functional equation with given matrices Q 1, Q 2 and vectorL, where each function h 1 and h 2 is algebraically defined on a rational cubic curve. The solutionM is then represented by a series expansion involving the semi-group generated by the pair of functions h 1 and h 2 . This series expansion together with analytic continuation properties of the solutionM enables us to calculate the empty queue probabilities, the mean queue occupancies and to characterize the tail behavior of the workload distribution at each queue. Regarding the application to congestion control in telecommunication networks, our analysis shows that, without explicit marking, the SQF discipline yields a good performance in terms of mean waiting time for flows with a small contribution to the global load; this discipline may, however, have adverse effects for very large values of the waiting time, with tail asymptotics similar to that for the lowest priority flow of an HoL system.