Keynote
On Queues with Working Breakdown and Interdependence Between Arrival and Service Processes
In this talk, we consider a single server queueing system with working breakdown. The arrival and service processes evolve through transitions on the product space of two Markov chains. Thus the arrival and service processes are interdependent. The transitions in the product space are governed by a semi-Markov rule with sojourn times in states exponentially distributed. Server failure occurs according to a Poisson process with rate gamma γ. The repair time of the server follows exponential distribution with parameter beta β . During the working breakdown, the server continues serving the customers, but at a low rate. Simultaneously repair of the server is done. When the repair is completed, the server resumes normal service. We analyse this model using the matrix geometric method. Numerical illustrations are provided.