Octave package for Queueing Networks and Markov chains analysis: qsammm

Function Reference: `qsammm`

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

Compute $appro×imate$ 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

Function Reference: qsammm

Function Reference: `qsammm`