Some New Results for Departure Process in theMX/G/1 Queueing System with a Single Vacation and Exhaustive Service

Wojciech Michal Kempa

28 citations0/0 files storedStochastic Analysis and Applications

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

A batch arrival queueing system with a single vacation between two successive busy periods and with exhaustive service is considered. The departure process h(t) is studied first on a single vacation cycle. The approach based on renewal theory is applied to obtain results in the general case. In particular, the explicit representation for the generating function of Laplace transform of the probability function of h(t) is derived. All formulae are written in terms of input parameters of the system and factors of a certain canonical factorization of Wiener–Hopf type. A numerical approach to results is discussed as well.

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1980Stochastic Storage Processes 1986On the Mx/G/1 queue with vacation time 2002A batch arrival queue with a vacation time under single vacation policy

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2013Genetic Cost Optimization of the GI/M/1/N Finite-Buffer Queue with a Single Vacation Policy 2013On Applying Cuckoo Search Algorithm to Positioning GI/M/1/N Finite-Buffer Queue with a Single Vacation Policy 2015Transient workload distribution in the $$M/G/1$$ M / G / 1 finite-buffer queue with single and multiple vacations 2011Analysis of Departure Process in Batch Arrival Queue with Multiple Vacations and Exhaustive Service 2010The transient analysis of the queue-length distribution in the batch arrival system with N-policy, multiple vacations and setup times 2016A comprehensive study on the queue-size distribution in a finite-buffer system with a general independent input flow 2015An Application of Differential Evolution to Positioning Queueing Systems 2014On transient queue-size distribution in the batch-arrivals system with a single vacation policy

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