Consider a B&D queuing system which has a finite number of states denoted by n = 0, 1, 2, 3, 4. The arrival rates are = 4 for = 0, 1, 2, 3. The service rates are = for = 1, 2, 3, 4. Both rates are expressed

using the same time unit such as arrivals and services per week.

(a) Give an example of a queuing system which can be described by these arrival and service rates.

(b)Calculatethesteady-stateprobabilities{Pn}ofthesystemstatesusingthegeneralapproachdiscussed in class, as well as in the textbook. Determine the expected queue length, the expected arrival rate, and the expected waiting time.

(c) Consider this queuing system in its steady-state condition. We assume that if the system is in state n, then the system cost per day is f() = 2 (costs are expressed in thousands of dollars). Determine the expected system cost per day.