State space approach for solving transient queuing systems. (English) Zbl 1315.90010

Summary: We consider a transient queuing system and find its solution using the state space approach. For this, the given interval of study \([0,T]\) is subdivided into small subintervals, where it is reasonable to assume that the instantaneous arrival and service rates are constants. The system of equations together with the initial conditions is solved for an analytical expression for \(P_n\)’s in each interval. The solution obtained at the right end point of the previous subinterval is taken as the initial condition in the subsequent interval. The developed method is illustrated for an \((M/M/1):(FCFS/m/\infty)\) system.


90B22 Queues and service in operations research
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems