Analysis of a Two-Phase Queueing System with Impatient Customers and Multiple Vacations
نویسندگان
چکیده
In this paper, we consider a two-phase queueing system with impatient customers and multiple vacations. Customers arrive at the system according to a Poisson process. They receive the first essential service as well as a second optional service. Arriving customers may balk with a certain probability and may depart after joining the queue without getting service due to impatience. Lack of service occurs when the server is on vacation or busy during the first phase of service. We analyze this model and derive the probability generating functions for the number of customers present in the system for various states of the server. We further obtain the closed-form expressions for various performance measures including the mean system sizes for various states of the server, the average rate of balking, the average rate of reneging, and the average rate of loss.
منابع مشابه
Discrete Time Analysis of Multi-Server Queueing System with Multiple Working Vacations and Reneging of Customers
This paper analyzes a discrete-time $Geo/Geo/c$ queueing system with multiple working vacations and reneging in which customers arrive according to a geometric process. As soon as the system gets empty, the servers go to a working vacations all together. The service times during regular busy period, working vacation period and vacation times are assumed to be geometrically distributed. Customer...
متن کاملAnalysis of an M/M/1 Queueing System with Impatient Customers and a Variant of Multiple Vacation Policy
In this paper, we consider an M/M/1 queueing system with impatient customers and a variant of multiple vacation policy, where we examine the case that customer impatience is due to the servers’ vacation. Whenever a system becomes empty, the server takes a vacation. However, the server is allowed to take a maximum number of vacations, denoted by K vacations, if the system remains empty after the...
متن کاملSynchronized reneging in queueing systems with vacations
In this paper we present a detailed analysis of queueing models with vacations and impatient customers, where the source of impatience is the absence of the server. Instead of the standard assumption that customers perform independent abandonments, we consider situations where customers abandon the system simultaneously. This is, for example, the case in remote systems where customers may decid...
متن کاملAnalysis of Finite Buffer Markovian Queue with Balking, Reneging and Working Vacations
This article presents the analysis of a finite buffer M/M/1 queue with multiple and single working vacations. The arriving customers balk (that is do not join the queue) with a probability and renege (that is leave the queue after joining) according to exponential distribution. The inter-arrival times, service times during a regular service period, service times during a vacation period and vac...
متن کاملBat Algorithm for Optimal Service Parameters in an Impatient Customer N-Policy Vacation Queue
In this paper, a meta-heuristic method, the Bat Algorithm, based on the echolocation behavior of bats is used to determine the optimum service rate of a queue problem. A finite buffer M/M/1 queue with N policy, multiple working vacations and Bernoulli schedule vacation interruption is considered. Under the two customers' impatient situations, balking and reneging, the...
متن کامل