Program/Track B/B.1.2/On A Queue With Marked Compound Poisson Input And Exponentially Distributed Batch Service
On A Queue With Marked Compound Poisson Input And Exponentially Distributed Batch Service
Khamis Abdullah Khamis AL Maqbali, Varghese C. Joshua, Achyutha Krishnamoorthy
In this paper, we consider the batch arrival with batch service process. We assume that our queueing model has multi-server. Arrivals of customers in batches of various sizes (1,2,...,k ) form a marked compound Poisson process; we designate the batches as T1,T2,...,Tk. The service time of Ti follows exponential distribution with parameter mu i, i=1,2,...,k; they are served in batches of the specific size. In arrival process, waiting room of type i for Ti has finite capacity except waiting room of type 1 for T1. In service process, server room of type i has finite capacity. Ti can go to service if server room of type i has available space. If server room of type i does not have available place, then there are two following cases. The first case, if waiting room of type i has available places, Ti must wait in this waiting room. The second case, if waiting room of type i does not have available place, then Ti must leave the system without service except T1, who must wait in waiting room of type 1. Various performance measures are estimated.