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Mixed polling with rerouting and applications

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Title Mixed polling with rerouting and applications
 
Creator KAVITHA, V
COMBES, R
 
Subject Continuous polling systems
Rerouting
Virtual workload
Pseudo conservation laws
Local area network
SPATIALLY DISTRIBUTED ARRIVALS
SYSTEMS
QUEUES
MODELS
 
Description Queueing systems with a single server in which customers wait to be served at a finite number of distinct locations (buffers/queues) are called discrete polling systems. Polling systems in which arrivals of users occur anywhere in a continuum are called continuous polling systems. Often one encounters a combination of the two systems: the users can either arrive in a continuum or wait in a finite set (i.e. wait at a finite number of queues). We call these systems mixed polling systems. Also, in some applications, customers are rerouted to a new location (for another service) after their service is completed. In this work, we study mixed polling systems with rerouting. We obtain their steady state performance by discretization using the known pseudo conservation laws of discrete polling systems. Their stationary expected workload is obtained as a limit of the stationary expected workload of a discrete system. The main tools for our analysis are: (a) the fixed point analysis of infinite dimensional operators and; (b) the convergence of Riemann sums to an integral. We analyze two applications using our results on mixed polling systems and discuss the optimal system design. We consider a local area network, in which a moving ferry facilitates communication (data transfer) using a wireless link. We also consider a distributed waste collection system and derive the optimal collection point. In both examples, the service requests can arrive anywhere in a subset of the two dimensional plane. Namely, some users arrive in a continuous set while others wait for their service in a finite set. The only polling systems that can model these applications are mixed systems with rerouting as introduced in this manuscript. (C) 2013 Elsevier B.V. All rights reserved.
 
Publisher ELSEVIER SCIENCE BV
 
Date 2014-10-16T06:46:40Z
2014-10-16T06:46:40Z
2013
 
Type Article
 
Identifier PERFORMANCE EVALUATION, 70(11)1001-1027
0166-5316
1872-745X
http://dx.doi.org/10.1016/j.peva.2013.08.020
http://dspace.library.iitb.ac.in/jspui/handle/100/15470
 
Language en