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Analysis of a dynamic assignment of impatient customers to parallel queues

Movaghar, A ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1007/s11134-010-9207-9
  3. Abstract:
  4. 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
  5. Keywords:
  6. Analytical models ; Dynamic policy ; Impatient customers ; Parallel queues
  7. Source: Queueing Systems ; Volume 67, Issue 3 , 2011 , Pages 251-273 ; 02570130 (ISSN)
  8. URL: http://link.springer.com/article/10.1007%2Fs11134-010-9207-9