This paper considers a queuing system which facilitates a single server that serves two classes of units: high priority and low priority units. These two classes of units arrive at the system in two independent compound Poisson processes. It aims to decipher average queue size and average waiting time of the units. Under the pre-emptive priority rule, the server provides a general service to these arriving units. It is further assumed the server may take a vacation after serving the last high priority unit present in the system or at the service completion of each low priority unit present in the system. Otherwise, he may remain in the system. Also, if a high priority unit is not satisfied with the service given it may join the tail of the queue as a feedback unit or leave the system. The server may break down exponentially while serving the units. The repair process of the broken server is not immediate. There is a delay time to start the repair. The delay time to repair and repair time follow general distributions. We consider reneging to occur for the low priority units when the server is unavailable due to breakdown or vacation. We concentrate on deriving the transient solutions by using supplementary variable technique. Further, some special cases are also discussed and numerical examples are presented.
Ayyappan, G. and Udayageetha, J.
Transient Solution of M[X1],M[X2]/G1,G2/1 with Priority Services, Modified Bernoulli Vacation, Bernoulli Feedback, Breakdown, Delaying Repair and Reneging,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 12,
2, Article 1.
Available at: https://digitalcommons.pvamu.edu/aam/vol12/iss2/1