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A mathematical programming approach to optimal Markovian switching of Poisson arrival streams to queueing systems

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Title A mathematical programming approach to optimal Markovian switching of Poisson arrival streams to queueing systems
 
Creator HEMACHANDRA, N
NARAHARI, Y
 
Subject markov modulated poisson process
admission control in queues
linear and nonlinear programming
global optimization
 
Description Motivated by certain situations in manufacturing systems and communication networks, we look into the problem of maximizing the profit in a queueing system with linear reward and cost structure and having a choice of selecting the streams of Poisson arrivals according to an independent Markov chain. We view the system as a MMPP/GI/1 queue and seek to maximize the profits by optimally choosing the stationary probabilities of the modulating Markov chain. We consider two formulations of the optimization problem. The first one (which we call the PUT problem) seeks to maximize the profit per unit time whereas the second one considers the maximization of the profit per accepted customer (the PAC problem). In each of these formulations, we explore three separate problems. In the first one, the constraints come from bounding the utilization of an infinite capacity server; in the second one the constraints arise from bounding the mean queue length of the same queue; and in the third one the finite capacity of the buffer reflect as a set of constraints. In the problems bounding the utilization factor of the queue, the solutions are given by essentially linear programs, while the problems with mean queue length constraints are linear programs if the service is exponentially distributed. The problems modeling the finite capacity queue are non-convex programs for which global maxima can be found. There is a rich relationship between the solutions of the PUT and PAC problems. In particular, the PUT solutions always make the server work at a utilization factor that is no less than that of the PAC solutions.
 
Publisher KLUWER ACADEMIC PUBL
 
Date 2011-08-17T02:57:10Z
2011-12-26T12:55:18Z
2011-12-27T05:44:04Z
2011-08-17T02:57:10Z
2011-12-26T12:55:18Z
2011-12-27T05:44:04Z
2000
 
Type Article
 
Identifier QUEUEING SYSTEMS, 36(4), 443-461
0257-0130
http://dx.doi.org/10.1023/A:1010983510051
http://dspace.library.iitb.ac.in/xmlui/handle/10054/9716
http://hdl.handle.net/10054/9716
 
Language en