Single-Server Queueing System with a Simple Input Process and a Service Time Dependent on the Waiting Time

A single-server queueing system with a Poisson input process and a service time that depends on the waiting time is analyzed. An integrodifferential equation is derived for the virtual waiting-time distribution function, and a method is proposed for its solution. The solution of the well-known Barrer problem is discussed as a special case of the investigated model.