Analysis of An M/G/1 Retrial G-Queue With Various Types of Customers Under Working Vacation
DOI:
https://doi.org/10.67440/ahj.vi.2592Keywords:
Retrial queue, priority queue, negative customers, working vacations, supplementary variable technique.Abstract
Consider a single server retrial queueing system with preemptive priority service and single working vacation in which two types of customers arrive in a Poisson process with arrival rates. (i) ordinary customers (ii) for high level Priority customers, we assumed that regular service times follows an exponential distribution with parameters 1 and 2. The retrial is introduced for low priority customers only. During working vacation the server serve’s the arriving customers with less service rates 3 and 4.
An M/G/1 retrial G-queue with preemptive priority for primary customers models a single –server system where high- priority primary customers immediately interrupt regular service, while low-priority (or) blocked customers enter a retrial orbit and negative customers (“G-Customers”).
The negative customer is arriving during the service time of any positive customer, will remove the positive customer from the service. If the interrupted customer is an ordinary customer, he will leave the system. As soon as the orbit becomes empty at the time of service completion, the server goes for a working vacation. The server works at a lower speed during a working vacation period.
Using the supplementary variable technique, the steady –state probability generating a function of the system and its orbit are found some numerical examples are presented.
