Time dependent system state probabilities of single server queuing system with infinite queue

Abstract

Analytical expression for time dependent system state probabilities of single server queuing system with infinite queue capacity M/M/1 is derived. Expression is derived by finding the limit value of expression for time dependent system state probabilities of single server queuing system with finite queue capacity M/M/1/K, when number of places in the queue tens to infinity, in the case that system is empty at the beginning. Only elementary mathematical operations are used.

Keywords

• time dependent probabilities
• m/m/1 queuing system
• infinite capacity