Abstract

Analysis and Comparative Study of Various Performance Measures of M/G/1 and M/G/S Queuing Models

Pradeep K. Joshi1*, Shejal Gupta2 and K. N. Rajeshwari3

1Reader, Department of Mathematics, IPS Academy, Indore, INDIA. 2Research Scholar, School of Mathematics, DAVV, Indore, INDIA. 3Professor & Head, School of Mathematics, DAVV, Indore, INDIA.

DOI : http://dx.doi.org/10.29055/jcms/982

ABSTRACT

Queuing theory is a mathematical tool, which deals with the phenomenon of waiting lines. Keeping customers waiting for too long, affects various parameters of queuing theory. In this paper, optimization technique has been applied to calculate the performance measures like waiting time, traffic intensity, waiting cost and proportion of time the server is idle for single server M/G/1 model as well as for multiple servers M/G/S model. Also, we analysis the comparative study of various performance measures of single server M/G/1 model and multiple servers M/G/S queuing model. This investigation deals with M/G/1 and M/G/S Models in which arrival follows Poisson distribution, service time follows general distribution, and Queue discipline is FCFS. The result of analysis showed that as we increase the number of servers, the waiting time in the queue decreases, total cost of the system decreases, traffic intensity also decreases whereas idle time increases. The results are optimize and effective. The graphical representation of various performance measures and their comparison are shown by MATLAB software.

Keywords :M/G/1 Model, M/G/S Model, Queue, Traffic Intensity, waiting time, waiting cost, service cost.

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