Function File: [U, R, Q, X] = qsammm (lambda, mu)

Compute approximate utilization, response time, average number of requests in service and throughput for an asymmetric M/M/m queue. In this type of system there are m different servers connected to a single queue. Each server has its own (possibly different) service rate. If there is more than one server available, requests are routed to a randomly-chosen one.

INPUTS

lambda

Arrival rate (lambda>0)

mu

mu(i) is the service rate of server i, 1 ≤ i ≤ m. The system must be ergodic (lambda < sum(mu)).

OUTPUTS

U

Approximate service center utilization, U = \lambda / ( \sum_{i=1}^m \mu_i ).

R

Approximate service center response time

Q

Approximate number of requests in the system

X

Approximate system throughput. If the system is ergodic, X = lambda

REFERENCES

• G. Bolch, S. Greiner, H. de Meer and K. Trivedi, Queueing Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications, Wiley, 1998

See also: qsmmm.

Package: queueing