Two parallel finite queues with simultaneous services and Markovian arrivals
type: Item
instance of: scholarly article
title: Two parallel finite queues with simultaneous services and Markovian arrivals
zbMATH Open document ID: 0896.60066
DOI: 10.1155/S1048953397000439
author: J. Ning
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 1998-10-01T00:00:00Z
full work available at URL: https://eudml.org/doc/47978
review text: Summary: We consider a finite capacity single server queueing model with two buffers, \(A\) and \(B\), of sizes \(K\) and \(N\), respectively. Messages arrive one at a time according to a Markovian arrival process. Messages that arrive at buffer \(A\) are of a different type from the messages that arrive at buffer \(B\). Messages are processed according to the following rules: 1. When buffer \(A\) \((B)\) has a message and buffer \(B\) \((A)\) is empty, then one message from \(A\) \((B)\) is processed by the server. 2. When both buffers, \(A\) and \(B\), have messages, then two messages, one from \(A\) and one from \(B\), are processed simultaneously by the server. The service times are assumed to be exponentially distributed with parameters that may depend on the type of service. This queueing model is studied as a Markov process with a large state space and efficient algorithmic procedures for computing various system performance measures are given. Some numerical examples are discussed.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60K20
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 60K05
Mathematics Subject Classification ID: 60K15
zbMATH DE Number: 1124520
zbMATH Keywords: Markov chains
zbMATH Keywords: Markovian arrival process
zbMATH Keywords: renewal process
zbMATH Keywords: queues
zbMATH Keywords: finite capacity
zbMATH Keywords: exponential services
zbMATH Keywords: algorithmic probability
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1124520