In this investigation, the steady state analysis of two individualistic batch arrival queues with immediate feedback, modified Bernoulli vacation and server breakdown are introduced. Two different categories of customers like priority and ordinary are to be considered. This model propose nonpreemptive priority discipline. Ordinary and priority customers arrive as per Poisson processes. The server consistently afford single service for priority customers and the general bulk service for the ordinary customers and the service follows general distribution. The ordinary customers to be served only if the batch size should be greater than or equal to "a", else the server should not start service until "a" customers have accumulated. Meanwhile priority queue is empty; the server becomes idle or go for vacation. If server gets breakdown while the priority customers are being served, they may wait in the head of the queue and get fresh service after repair completion, but in case of ordinary customers they may leave the system. After completion of each priority service, customer may rejoin the system as a feedback customer for receiving regular service because of inappropriate quality of service. Supplementary variable technique and probability generating function are generally used to solve the Laplace transforms of time-dependent probabilities of system states. Finally, some performance measures are evaluated and express the numerical results.
Ayyappan, G.; Nithya, S.; and Somasundaram, B.
(R1984) Analysis of M^[X1], M^[X2]/G1, G_2^(a,b)/1 Queue with Priority Services, Server Breakdown, Repair, Modified Bernoulli Vacation, Immediate Feedback,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 17,
2, Article 1.
Available at: https://digitalcommons.pvamu.edu/aam/vol17/iss2/1