G/G/s Queueing System
To see the effect of the variation of demand and variation of service rate, you may use the G/G/s queuing calculator below. For arrival to be Poisson Distribution set Mean Arrival rate = Standard deviation of Arrival rate. For service time to be Exponentially Distribution , set mean service rate = Standard deviation of service rate. For Deterministic arrival rate or service rate, standard deviation is set to zero.
The formulas of the measurement of effectiveness for the queuing calculator is given below based Allen and Cunneen's approximation of G/G/s where the basic formula is M/M/s.
- Arrival rate (number of customers/unit time)
- Mean Service rate (number of customers/unit time)
- Coefficient of variation for inter-arrival time
- Coefficient of variation for service time
- Wq = average time a customer spends in waiting line waiting for service,
- W = average time a customer spends in the system (in waiting line and being served),
- Lq = average number of customer in waiting line for service,
- For G/G/1, this becomes
- L = average number of customer in the system (in waiting line and being served),
Preferable reference for this tutorial is
Teknomo, Kardi. (2014) Queuing Theory Tutorial