Town Taxi uses three dispatchers to handle requests for service and to dispatch the cabs. The telephone calls that are made to Town Taxi use a common number. When all dispatchers are busy, the caller hears a waiting song until the first dispatchers becomes available. The telephone system will assign available dispatcher to the waiting callers according to FCFS. Assume that the arrival of calls follows a Poisson distribution, with an average of 35 calls per hour. Also assume that the time that each dispatcher spends with a customer follows Exponential distribution and each dispatcher takes an average of 3 minutes with each caller. a What percentage of time all dispatchers are idle? b What percentage of time only one dispatcher is busy? c. What is the average number of callers in the system?
Town Taxi uses three dispatchers to handle requests for service and to dispatch the cabs. The telephone calls that are made to Town Taxi use a common number. When all dispatchers are busy, the caller hears a waiting song until the first dispatchers becomes available. The telephone system will assign available dispatcher to the waiting callers according to FCFS. Assume that the arrival of calls follows a Poisson distribution, with an average of 35 calls per hour. Also assume that the time that each dispatcher spends with a customer follows Exponential distribution and each dispatcher takes an average of 3 minutes with each caller.
a What percentage of time all dispatchers are idle?
b What percentage of time only one dispatcher is busy?
c. What is the average number of callers in the system?
d What is the average time in minutes that a customer spends in the system?
e What is the total cost of the system for 8 hours if each dispatcher charges $25 /hour and the waiting cost per hour for each customer is $30.
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