# Question: People s Software Company has just set up a call center

People’s Software Company has just set up a call center to provide technical assistance on its new software package. Two technical representatives are taking the calls, where the time required by either representative to answer a customer’s questions has an exponential distribution with a mean of 8 minutes. Calls are arriving according to a Poisson process at a mean rate of 10 per hour.

By next year, the mean arrival rate of calls is expected to decline to 5 per hour, so the plan is to reduce the number of technical representatives to one then.

T (a) Assuming that μ will continue to be 7.5 calls per hour for next year’s queueing system, determine L, Lq, W, and Wq for both the current system and next year’s system. For each of these four measures of performance, which system yields the smaller value?

(b) Now assume that μ will be adjustable when the number of technical representatives is reduced to one. Solve algebraically for the value of μ that would yield the same value of W as for the current system.

(c) Repeat part (b) with Wq instead of W.

By next year, the mean arrival rate of calls is expected to decline to 5 per hour, so the plan is to reduce the number of technical representatives to one then.

T (a) Assuming that μ will continue to be 7.5 calls per hour for next year’s queueing system, determine L, Lq, W, and Wq for both the current system and next year’s system. For each of these four measures of performance, which system yields the smaller value?

(b) Now assume that μ will be adjustable when the number of technical representatives is reduced to one. Solve algebraically for the value of μ that would yield the same value of W as for the current system.

(c) Repeat part (b) with Wq instead of W.

**View Solution:**## Answer to relevant Questions

Consider a generalization of the M/M/1 model where the server needs to “warm up” at the beginning of a busy period, and so serves the first customer of a busy period at a slower rate than other customers. In particular, ...Consider the finite queue variation of the M/M/s model. Derive the expression for Lq given in Sec. 17.6 for this model. Consider the following statements about an M/G/1 queueing system, where 2 is the variance of service times. Label each statement as true or false, and then justify your answer. (a) Increasing σ2 (with fixed λ and μ) will ...Consider the E2/M/1 model with λ = 4 and μ = 5. This model can be formulated in terms of transitions that only involve exponential distributions by dividing each interarrival time into two consecutive phases, each having ...Reconsider the queueing system described in Prob. 17.4-6. Suppose now that type 1 customers are more important than type 2 customers. If the queue discipline were changed from first-come-first-served to a priority system ...Post your question