Queueing analysis of a contention-based service system

In this paper, we consider a single-server service system with contention periods preceding the service operation. Customer interarrival times are exponentially distributed with a rate that depends on the current system occupancy, and customers must be successful in the contention phase in order to obtain access to the service phase. There are C contention slots in each contention period, which are chosen at random by the contending customers, and success is determined by a capture model. Each contention period is followed by S service periods. Customers who have already contended successfully receive service on a FCFS basis, and service times are drawn independently from a discrete distribution. We model the system as a Markov renewal process embedded at departure service times. We solve the model and then compute the equilibrium distributions of the number of customers in the system at an arbitrary point in time and at customer arrival epochs. Finally, we give numerical examples that show the effects of contention on system performance.