Time dependence of queues with semi-Markovian services

Erhan Çınlar

62 citations0/0 files storedJournal of Applied Probability

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

Abstract

A single server queueing system with Poisson input is considered. There are a finite number of types of customers and the service time of the nth customers depends on the types of the nth and the (n – l)th customers. The time dependence of the queue size process will be studied, (it will be clear how the methods of the paper can be applied to other processes of interest,) and limiting as well as transient results will be given.

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1963Introduction to the Theory of Queues.1966The single server queue with Poisson input and semi-Markov service times

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1984On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian Environment 1997Non-Skip-Free M/G/ 1 and G/M/ 1 Type Markov Chains 1986Generalizations of the Pollaczek-Khinchin integral equation in the theory of queues 1972On the use of a fundamental identity in the theory of semi-Markov queues 1995Linear independence of root equations forM/G/1 type Markov chains 1974The Markov Renewal Branching Process 1975Random Flow in Queueing Networks: A Review and Critique 2006Fundamental characteristics of queues with fluctuating load

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