Mobile telecommunications requests arrive at a cellular site exchange center such that the density of requests follow the following pattern: Frequency 300 requests 700 requests 1,200 requests Average processing time 30 secs/request 10 secs/request 5 secs/request Each request is routed to one of the eight parallel processors in the cellsite tower, each of which has the same processor speed following an exponential distribution. Each processor finishes each request before it takes on another request. When all the processors are engaged with requests, then a "busy" signal is returned to any arriving request.

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Chapter1: Combinatorial Analysis
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Mobile
telecommunications requests arrive at a cellular site exchange center such that
the density of requests follow the following pattern:
Frequency
300 requests
700 requests
1,200 requests
Average processing time
30 secs/request
10 secs/request
5 secs/request
Each request is routed to one of the eight parallel processors in the cellsite tower, each
of which has the same processor speed following an exponential distribution. Each
processor finishes each request before it takes on another request. When all the
processors are engaged with requests, then a "busy" signal is returned to any arriving
request.
a) What is the expected probability that a busy signal would be returned by the
cellsite?
b) A proposed expansion will double the capacity such that the cellsite could have the
capacity of 16 parallel processors. If a service rate of 98% is the objective for traffic,
how many of the processors are deemed "excess" capacity?
Transcribed Image Text:Mobile telecommunications requests arrive at a cellular site exchange center such that the density of requests follow the following pattern: Frequency 300 requests 700 requests 1,200 requests Average processing time 30 secs/request 10 secs/request 5 secs/request Each request is routed to one of the eight parallel processors in the cellsite tower, each of which has the same processor speed following an exponential distribution. Each processor finishes each request before it takes on another request. When all the processors are engaged with requests, then a "busy" signal is returned to any arriving request. a) What is the expected probability that a busy signal would be returned by the cellsite? b) A proposed expansion will double the capacity such that the cellsite could have the capacity of 16 parallel processors. If a service rate of 98% is the objective for traffic, how many of the processors are deemed "excess" capacity?
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