Equilibrium customer strategies in a single server Markovian queue with setup times

Burnetas, Apostolos; Economou, Antonis

doi:10.1007/s11134-007-9036-7

Cited by 169 publications

(87 citation statements)

References 17 publications

(18 reference statements)

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“…Our contribution is in analyzing the effect of the dedicated band pricing on the (non-cooperative) behavior of SUs. Recently, [8,33] studied the decision process of customers who may join a server that can go on vacation. Under that model, the server stops serving customers for some (stochastically distributed) period, whenever it becomes idle.…”

Section: Related Workmentioning

confidence: 99%

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Non-Cooperative Spectrum Access — The Dedicated vs. Free Spectrum Choice

Jagannathan

Menache

Modiano

et al. 2012

IEEE J. Select. Areas Commun.

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We consider a dynamic spectrum access system in which Secondary Users (SUs) choose to either acquire dedicated spectrum or to use spectrum-holes (white spaces) which belong to Primary Users (PUs). The tradeoff incorporated in this decision is between immediate yet costly transmission and free but delayed transmission (a consequence of both the possible appearance of PUs and sharing the spectrum holes with multiple SUs). We first consider a system with a single PU band, in which the SU decisions are fixed. Employing queueing-theoretic methods, we obtain explicit expressions for the expected delays associated with using the PU band. Based on that, we then consider self-interested SUs and study the interaction between them as a noncooperative game. We prove the existence and uniqueness of a symmetric Nash equilibrium, and characterize the equilibrium behavior explicitly. Using our equilibrium results, we show how to maximize revenue from renting dedicated bands to SUs. Finally, we extend the scope to a scenario with multiple PUs, show that the band-pricing analysis can be applied to some special cases, and provide numerical examples.

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Section: Related Workmentioning

confidence: 99%

“…In other words, it is optimal to price the spectrum at the highest value that leads to the equilibrium pair (1,0). 8 Since we are interested in the revenue generated, the delay cost α/µ is not considered. Proof.…”

Section: Optimal Band Pricingmentioning

confidence: 99%

Non-Cooperative Spectrum Access — The Dedicated vs. Free Spectrum Choice

Jagannathan

Menache

Modiano

et al. 2012

IEEE J. Select. Areas Commun.

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“…In recent years, there exists an increasing trend on studying customers' strategic behavior in queues with vacations/breakdowns, in which positive externalities and FTC behavior are observed. Burnetas and Economou (2007) study a system with an exponential setup time when the server starts a new busy period. They consider customers' strategic behavior under different levels of information which may include the queue length and/or the state of the server (during setup or busy).…”

Section: Introductionmentioning

confidence: 99%

Strategic Behavior and Social Optimization in Markovian Vacation Queues

Guo

Hassin

2011

Operations Research

145

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We consider a single server queueing system in which service shuts down when no customers are present, and is resumed when the queue length reaches a given critical length. We assume customers are heterogeneous on delay sensitivity and analyze customers' strategic response to this mechanism and compare it to the overall optimal behavior. We provide algorithms to compute the equilibrium arrival rates and also derive the monotonicity of equilibrium and optimal arrival rates. We show that there may exist multiple equilibria in such a system and the optimal arrival rate may be larger or smaller than the decentralized equilibrium one.

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“…18, of the M/M/1 queue with setup times in Ref. 5, and of the M/M/1 queue with server's breakdowns in Ref. 6.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium customer strategies and social-profit maximization in the single-server constant retrial queue

Economou¹,

Kanta²

2011

Naval Research Logistics

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Abstract:We consider the single-server constant retrial queue with a Poisson arrival process and exponential service and retrial times. This system has not waiting space, so the customers that find the server busy are forced to abandon the system, but they can leave their contact details. Hence, after a service completion, the server seeks for a customer among those that have unsuccessfully applied for service but left their contact details, at a constant retrial rate. We assume that the arriving customers that find the server busy decide whether to leave their contact details or to balk based on a natural reward-cost structure, which incorporates their desire for service as well as their unwillingness to wait. We examine the customers' behavior, and we identify the Nash equilibrium joining strategies. We also study the corresponding social and profit maximization problems. We consider separately the observable case where the customers get informed about the number of customers waiting for service and the unobservable case where they do not receive this information. Several extensions of the model are also discussed.

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Equilibrium customer strategies in a single server Markovian queue with setup times

Cited by 169 publications

References 17 publications

Non-Cooperative Spectrum Access — The Dedicated vs. Free Spectrum Choice

Non-Cooperative Spectrum Access — The Dedicated vs. Free Spectrum Choice

Strategic Behavior and Social Optimization in Markovian Vacation Queues

Equilibrium customer strategies and social-profit maximization in the single-server constant retrial queue

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