A business center wants to lease a fax machine for customers to use. A regular f

Question

A business center wants to lease a fax machine for customers to use.  A regular fax machine leases for 12$ per hour, and it takes a customer an average of 6 minutes (exponentially distributed) to complete a faxing job.  An upgraded fax machine leases for 16$ per hour, and it reguires an average of 5 minutes to complete a faxing job.  Customers arrive at teh faxing machine at a rate of 8 per hour ( Poisson distributed), and a customer's time is valued at 8$ per hour.  Determine whihc fax machine the business center should lease.

Explanation / Answer

We can find this solution by the help of queing theory,

Buisness centre should use tha fax machine in which the length of queue is small,

Given that:

FIRST CASE

Arrival rate,lamda=8/hour

Serrvice rate,u=6minutes=60/6=10/hour

SO queue length= lamda/u*lamda/u-lamda

=8/10*8/10-8

=0.8*4

=3.2

So 3.2 (approx. 3) customers are in queue if we use first type of machine

SECOND CASE

Arrival rate,lamda=8/hour

Serrvice rate,u=5minutes=60/5=12/hour

SO queue length= lamda/u*lamda/u-lamda

=8/12*8/12-8

=1.33

So queue length is less in SECOND CASE

Hence second one is preffered

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