Self-Service Queuing System
The best queue happens when we can let the customers behave as the servers. This type of self-service queuing system produces the minimum queue length and minimum delay.
The arrival distribution of customers follows Poisson distribution and the distribution for service time follows Exponential distribution.
The M/M/∞ queuing calculator is based on the following formulation:
- Arrival rate (number of customers/unit time)
- Service rate (number of customers/unit time)
- U= Utilization factor = percentage of the time that all servers are busy,
- P 0 = probability that there are no customers in the system,
- P n = probability that there are n customers in the system,
- W q = 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),
- L q = average number of customer in waiting line for service,
- 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