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. 14.What is the probability of receiving at least 2 callers (P(X2 2) in the system within 15 minutes? Hint: customer arrival in M/M/k system is also following the Poisson Distribution. You have the formula in single-server cheat sheet!

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Chapter1: Combinatorial Analysis
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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.
14.What is the probability of receiving at least 2 callers (P(X2 2) in the system within 15 minutes? Hint: customer
arrival in M/M/k system is also following the Poisson Distribution. You have the formula in single-server cheat
sheet!
Select one:
a. 99.84%
O b. 95.84%
O c. 66.16%
O d. 91.56%
Transcribed Image Text: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. 14.What is the probability of receiving at least 2 callers (P(X2 2) in the system within 15 minutes? Hint: customer arrival in M/M/k system is also following the Poisson Distribution. You have the formula in single-server cheat sheet! Select one: a. 99.84% O b. 95.84% O c. 66.16% O d. 91.56%
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