Abstract
This paper presents an analysis of balking and reneging in finite-buffer discrete-time single server queue with single and multiple working vacations. An arriving customer may balk with a probability or renege after joining according to a geometric distribution. The server works with different service rates rather than completely stopping the service during a vacation period. The service times during a busy period, vacation period, and vacation times are assumed to be geometrically distributed. We find the explicit expressions for the stationary state probabilities. Various system performance measures and a cost model to determine the optimal service rates are presented. Moreover, some queueing models presented in the literature are derived as special cases of our model. Finally, the influence of various parameters on the performance characteristics is shown numerically.
Highlights
Discrete-time queueing models with server vacations have been studied extensively in recent years by many researchers because these systems are better suited than their continuoustime counterparts to analyze and design digital transmitting systems
When the server returns from a single working vacation (SWV), it stays in the system waiting for customers to arrive instead of taking another working vacation
We present a recursive method to obtain the stationary-state probabilities for late arrival system with delayed access
Summary
Discrete-time queueing models with server vacations have been studied extensively in recent years by many researchers because these systems are better suited than their continuoustime counterparts to analyze and design digital transmitting systems. The customers either balk (i.e., decide not to join the queue) or renege (i.e., leave after joining the queue without getting served) The significance of this system emerges in many real life situations such as telephone services, computer and communication systems, production line systems, machine operating systems, inventory systems, and the hospital emergency rooms. At a vacation termination epoch, if the queue is nonempty, a regular service period begins with normal service rate; otherwise the server takes another vacation This vacation policy is called multiple working vacations (MWV). It appears to be more pragmatic that the balking and reneging behaviors are studied with working vacations in the discrete-time queuing models. This paper focuses on a finite buffer balking and reneging in discrete-time single server queue with single and multiple working vacations.
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