# Question

Consider a telephone system with three lines. Calls arrive according to a Poisson process at a mean rate of 6 per hour. The duration of each call has an exponential distribution with a mean of 15 minutes. If all lines are busy, calls will be put on hold until a line becomes available.

(a) Print out the measures of performance provided by the Excel template for this queueing system (with t = 1 hour and t = 0, respectively, for the two waiting time probabilities).

(b) Use the printed result giving P{Wq > 0} to identify the steadystate probability that a call will be answered immediately (not put on hold). Then verify this probability by using the printed results for the Pn.

(c) Use the printed results to identify the steady-state probability distribution of the number of calls on hold.

(d) Print out the new measures of performance if arriving calls are lost whenever all lines are busy. Use these results to identify the steady-state probability that an arriving call is lost.

(a) Print out the measures of performance provided by the Excel template for this queueing system (with t = 1 hour and t = 0, respectively, for the two waiting time probabilities).

(b) Use the printed result giving P{Wq > 0} to identify the steadystate probability that a call will be answered immediately (not put on hold). Then verify this probability by using the printed results for the Pn.

(c) Use the printed results to identify the steady-state probability distribution of the number of calls on hold.

(d) Print out the new measures of performance if arriving calls are lost whenever all lines are busy. Use these results to identify the steady-state probability that an arriving call is lost.

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