|Alternating service systems
| Maria Vlasiou , Ph.D.
H. Milton Stewart School of Industrial Systems Engineering, Georgia Institute of Technology
January 24, 2008
Motivated by applications in healthcare logistics and warehousing, we consider a system consisting of a server alternating between two service points. We are interested in the throughput of the system, which is closely related to the waiting time of the server. This waiting time satisfies an equation very similar to the classic Lindley's equation for the waiting time in a single-server queue. Contrary to Lindley's recursion, its main characteristic is that it is a non-increasing monotone function in its main argument. Our main goal is to derive a closed-form expression of the steady-state distribution of the waiting time, and thus of the throughput of the system. In general this is not possible, so we state sufficient conditions that allow us to do so. We analyse this Lindley-type equation under general assumptions and discuss various performance characteristics. Moreover, we compare this system to the classic single-server queue and to a system where the server is not obliged to alternate. Time permitting, we will propose a unifying model, which includes both this alternating-service model and the classic single-server queue as special cases.