Strategic queueing behavior for individual and social optimization in managing discrete time working vacation queue with Bernoulli interruption schedule

Abstract

In this paper, we consider a discrete time working vacation queue with a utility function for the reward of receiving the service and the cost of waiting in the system. A more flexible switching mechanism between low and regular service states is introduced to enhance the practical value of the working vacation queue. Under different precision levels of the system information, namely observable, almost unobservable and fully unobservable cases, the utility function is studied from both the individual customer's and the system administrator's points of view. By analyzing the steady-state behavior of the system, the associated optimal joining decisions under different information scenarios are obtained. We find that for the fully observable queue, the joining threshold for individual optimization may be less than the one for social optimization in working vacation period. A similar situation also appears in almost unobservable case. Such phenomenon is not possible for the classic first come first served queue due to the fact that there is no vacation time and thus will not cause large fluctuations in customers' conditional waiting time. Additionally, we also conduct some numerical comparisons to demonstrate the effect of the information levels as well as system parameters on customer joining behavior.

A discrete-time queueing system with three different strategies

“…Let us show that D(z) > 0 for z ∈ [0, 1) if and only if the stability condition (10) is fulfilled. With this end in view we consider the following function:…”

“…If we assume that a vacation is considered as an interruption of the system we note that the pioneer paper is [9] and from another point of view of service interruptions between low and regular service state we recommend the paper [10] where the authors introduce a more flexible mechanism to enhance the practical value of a working vacation.…”

Customer Strategic Joining Behavior in Markovian Queues with Working Vacations and Vacation Interruptions Under Bernoulli Schedule

“…More recently, Liu and Wang (2017) studied customer equilibrium strategies in a working vacation queue concerning the Bernoulli schedule. Yu and Alfa (2016) studied the strategic behavior in a discrete-time working vacation queue with a Bernoulli interruption schedule. For further studies and references on vacation queuing systems (without a cost structure), one may refer to Doshi (1986), Takagi (1991), and Tian and Zhang (2006).…”

Customers' joining behavior in an unobservable <i>GI/Geo/m</i> queue

“…Recently, Goswami and Panda [11] presented strategic customer behavior in discrete-time single server queues in both observable and unobservable cases. There are various literature available on strategic customer behavior in discrete-time single server queues with different variations such as server vacations (Gao and Wang [7], Ma et al [26]), interruption (Yu and Alfa [35]), batch service (Panda and Goswami [30]), pricing (Ma and Liu [27]), breakdown and repairs (Yang et al [33]). 1 presents the works that are available related to the game-theoretic analysis in single and multi-server queueing systems.…”