Function File: [U, R, Q, X, p0] = qsmh1 (lambda, mu, alpha)

Compute utilization, response time, average number of requests and throughput for a M/H_m/1 system. In this system, the customer service times have hyper-exponential distribution:

       ___ m
       \
B(x) =  >  alpha(j) * (1-exp(-mu(j)*x))   x>0
       /__ 
           j=1

where \alpha_j is the probability that the request is served at phase j, in which case the average service rate is \mu_j. After completing service at phase j, for some j, the request exits the system.

INPUTS

lambda

Arrival rate

mu

mu(j) is the phase j service rate. The total number of phases m is length(mu).

alpha

alpha(j) is the probability that a request is served at phase j. alpha must have the same size as mu.

OUTPUTS

U

Service center utilization

R

Service center response time

Q

Average number of requests in the system

X

Service center throughput

Package: queueing