Question

Ocala Software Systems operates a technical support center for its software customers. If customers have installation or use problems with Ocala software products, they may telephone the technical support center and obtain free consultation. Currently, Ocala operates its support center with one consultant. If the consultant is busy when a new customer call arrives, the customer hears a recorded message stating that all consultants are currently busy with other customers. The customer is then asked to hold and is told that a consultant will provide assistance as soon as possible. The customer calls follow a Poisson probability distribution, with an arrival rate of nine calls per hour. On average, it takes 7.5 minutes for a consultant to answer a customer's questions. The service time follows an exponential probability distribution. To improve customer service, Ocala Software Systems wants to investigate the effect of using a second consultant at its technical support center. What effect would the additional consultant have on customer service? Would two technical consultants enable Ocala to meet its service guidelines (no more than 35% of all customers having to wait for technical support and an average customer waiting time of two minutes or less)? Round your answers to two decimal places.

With two consultants, ___% of customers have to wait, with an average _____waiting time of minutes. Therefore, two consultants do not meet service goals.

Answer 1

This will be M/M/2 queue

lambda = 9 call/ hour

mu = 1 / 7.5 per minute = 60/7.5 per hour

= 8 / hour

rho = 9/16 = 0.5625

probability that customer have to wait

=1 - P0

= 0.72

Wq = 0.0579 hour = 3.474 minute