Paper Info
Title
Analysis of a dynamic assignment of impatient customers to parallel queues
Abstract
Consider a number of parallel queues, each with an arbitrary capacity and multiple identical exponential servers. The service discipline in each queue is first-come-first-served (FCFS). Customers arrive according to a state-dependent Poisson process. Upon arrival, a customer joins a queue according to a state-dependent policy or leaves the system immediately if it is full. No jockeying among queues is allowed. An incoming customer to a parallel queue has a general patience time dependent on that queue after which he/she must depart from the system immediately. Parallel queues are of two types: type 1, wherein the impatience mechanism acts on the waiting time; or type 2, a single server queue wherein the impatience acts on the sojourn time. We prove a key result, namely, that the state process of the system in the long run converges in distribution to a well-defined Markov process. Closed-form solutions for the probability density function of the virtual waiting time of a queue of type 1 or the offered sojourn time of a queue of type 2 in a given state are derived which are, interestingly, found to depend only on the local state of the queue. The efficacy of the approach is illustrated by some numerical examples.
Year
DOI
Venue
2011
10.1007/s11134-010-9207-9
Queueing Syst.
Keywords
Field
DocType
Analytical models,Dynamic policy,Impatient customers,Parallel queues,60K25,68M20,90B22
M/M/1 queue,Mathematical optimization,Bulk queue,M/M/c queue,Multilevel queue,Computer science,M/G/1 queue,M/G/k queue,Real-time computing,Queue management system,Fork–join queue
Journal
Volume
Issue
ISSN
67
3
0257-0130
Citations 
PageRank 
References 
0
0.34
9
Authors
1
Name
Order
Citations
PageRank
A. Movaghar119732.28