Analysis of Queue-Length Dependent Vacations and P-Limited Service in BMAP/G/1/N Systems: Stationary Distributions and Optimal Control. (10th November 2013)

• Record Type: Journal Article
• Authors: Banik, A. D.
• Other Names: Orsingher Enzo Academic Editor.
• Is Part Of: International journal of stochastic analysis. Volume 2013(2013)
• Publication Date: 2013-11-10
• Subjects: Stochastic analysis -- Periodicals; Stochastic analysis; Periodicals; 519.22
• DOI: 10.1155/2013/196372
• Languages: English
• ISSNs: 2090-3332

Abstract

Abstract : We consider a finite-buffer single server queueing system with queue-length dependent vacations where arrivals occur according to a batch Markovian arrival process (BMAP). The service discipline is P-limited service, also called E-limited with limit variation (ELV) where the server serves until either the system is emptied or a randomly chosen limit of L customers has been served. Depending on the number of customers present in the system, the server will monitor his vacation times. Queue-length distributions at various epochs such as before, arrival, arbitrary and after, departure have been obtained. Several other service disciplines like Bernoulli scheduling, nonexhaustive service, and E-limited service can be treated as special cases of the P-limited service. Finally, the total expected cost function per unit time is considered to determine locally optimal values N * of N or a maximum limit L ^ * of L ^ as the number of customers served during a service period at a minimum cost.