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Queueing Systems
Erschienen in: Queueing Systems 3-4/2020

16.11.2020

Strategic behavior and optimization in a hybrid M/M/1 queue with retrials

verfasst von: Yoav Kerner, Ophir Shmuel-Bittner

Erschienen in: Queueing Systems | Ausgabe 3-4/2020

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Abstract

In standard queues, when there are waiting customers, service completions are followed by service commencements. In retrial queues, this is not the case. In such systems, customers try to receive service at a time of their choosing, or the server seeks the next customer for a non-negligible time. In this note, we consider a hybrid model with both a finite standard queue and an orbit. While in the orbit, customers try to join the standard queue in their own time. We assume that the retrial rate is a decision variable, and study both the Nash equilibrium and the socially optimal retrial rates, under a cost model that considers both waiting costs and retrial costs.
Vorheriger Artikel Equilibrium points and equilibrium sets of some queues
Nächster Artikel Deterministic state-based information disclosure policies and social welfare maximization in strategic queueing systems

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Fußnoten
1
Alternatively, one may assume that service is associated with a significantly large reward, and hence this prohibition is actually a result.
 
2
Elcan’s notation is a bit different. He denotes the steady-state probability by \(\mu \) (here it is p), the service by \(\alpha \) (here it is \(\mu \)) and retrial rate by \(\gamma \) (here it is \(\eta \)). Also, one needs to set \(r=1\) to fit the result to the one we quote. In the case where \(r=1\), the sums can be simplified: see [12].
 
3
In practice, we solve the equations by truncating the state space and the capacity of the orbit to a large k. Alternatively, the partial generating functions can be evaluated numerically.
 
4
Kulkarni presented the parameters in a normalized mode: He set the retrial cost to be 1 (here it is r). He set the waiting cost to be per service time and not per time unit, and hence his C is our \(c\mu \). Kulkarni also assumed general service time, but in the exponential service times his \(\frac{\tau }{S}=\frac{1}{\sqrt{2}}\).
 
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Metadaten
Titel
Strategic behavior and optimization in a hybrid M/M/1 queue with retrials
verfasst von
Yoav Kerner
Ophir Shmuel-Bittner
Publikationsdatum
16.11.2020
Verlag
Springer US
Erschienen in
Queueing Systems / Ausgabe 3-4/2020
Print ISSN: 0257-0130
Elektronische ISSN: 1572-9443
DOI
https://doi.org/10.1007/s11134-020-09672-w

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