M/E_k/1 Queueing System with Working Vacation

Abstract

__________________________________________________________________________Abstract: This paper deals with state dependent M/E k /1 queueing system with server breakdown and working vacation. As soon as the system becomes empty, the server leaves the system and takes vacation for random duration during which it may perform ancillary duty and is called on working vacation. It is assumed that the server may breakdown when it is busy. The vacation duration and the life time of server are exponentially distributed. Both service times in a working vacation and in a busy period are assumed to be Erlangian distributed. Once server starts the service, he continues until all jobs are served. The Chapman Kolmogorov equations are constructed in order to obtain the steady state probability distribution of the number of jobs in the system. The probability generating function is employed to obtain the average queue length and other system characteristics. Numerical experiment is performed to validate the analytical results. The sensitivity analysis has been done to examine the effect of different parameters.

Mathematical Analysis of Queue with Phase Service: An Overview

“…A process with sequential phases gives rise to an Erlangian distribution depending upon whether or not the phases have identical distribution. Erlang distribution has been considered by Adan et al [1], Wang [2], Wang and Kuo [3], Jain and Agrawal [4], and many others in different frameworks. The design of Erlangian distribution is purely sequential as shown in Figure 1.…”

Modelling of Freight Trains Classification Using Queueing System Subject to Breakdowns

“…The server is so-called removable that means the system turns on and turns off the server in dependency on the number of customers in the system. Jain and Agrawal [4] also studied a single-server queueing system; they assumed the server takes vacation when it becomes idle and may break down when it is busy. The authors used the Erlang distribution for modelling service times.…”

Feedback of a Non-Truncated Erlang Queuing System with Balking and Retention of Reneged Customers

“…On a truncated Erlangian queueing system with state -dependent service rate, balking and reneging is obtained by Paoumy [7] using iterative method. Also, Madhu and Kumar [4] developed a M/E k /1 queueing system with working vacation. Other related studies are presented by Abid and Al -Madi [8], Kotb and Moamer [12], Mishra and Dinesh [6], Jayachitra and James Albert [10] and [11] and Jayachitra et al [9].…”