DES - Steady-State Conditions for Queuing Systems

Steady-State Conditions for Queuing Systems:

List of knowledge needed for this page:

• Definition of $S_q$ : system time of costumer $q$.
• Definition of $X(t)$: state at time t which being in a queuing system will also describe the number of customers in the system.

NOTE: $X$ and $S$ are defined as show in this page, such as the limits of system time and system state

We can use this limits to forget about the dependency of the system with time, saying: “At steady state the average number of customer in the system will be E$[X]$ and each customer will stay in the system E$[S]$ seconds/minutes/hours/… (it depends on how you declare $S_q$)”