Abstract
We consider the customers equilibrium and socially optimal joining-balking behavior in single-server Markovian queues with multiple working vacations and vacation interruptions. Arriving customers decide whether to join the system or balk, based on a linear reward-cost structure that incorporates their desire for service, as well as their unwillingness for waiting. We consider that the system states are observable, partially observable, and unobservable, respectively. For these cases, we first analyze the stationary behavior of the system and get the equilibrium strategies of the customers and compare them to socially optimal balking strategies numerically.
Highlights
In the past decades, there has been an emerging tendency in the literature to study queueing systems which are concerned with customers decentralized behavior and socially optimal control of arrivals
His study was complemented by Edelson and Hildebrand [2] who considered the same queueing system as that in [1] but assumed that the customers made their decisions without being informed about the state of the system
As for the work studying customers behavior in queueing systems with working vacations, Zhang et al [14] and Sun and Li [15] obtained equilibrium balking strategies in M/M/1 queues with working vacations for four cases with respect to different levels of information
Summary
There has been an emerging tendency in the literature to study queueing systems which are concerned with customers decentralized behavior and socially optimal control of arrivals. Sun and Tian [5] considered a queueing model with classical multiple vacations They derived the equilibrium and socially optimal joining strategies in vacation and busy period of a partially observable queue, respectively. Guo and Hassin [7] studied a vacation queue with N-policy and exhaustive service They presented the equilibrium and socially optimal strategies for unobservable and observable queues. As for the work studying customers behavior in queueing systems with working vacations, Zhang et al [14] and Sun and Li [15] obtained equilibrium balking strategies in M/M/1 queues with working vacations for four cases with respect to different levels of information. Sun et al [16] considered the customers equilibrium balking behavior in some single-server Markovian queues with two-stage working vacations.
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