a) What is the average time that a customer spends in the whole system? Time spent in the system = amount of time that the entity spent in the system from arrival to departure. b) What is the average waiting time in queue 1? in queue 2? Time in queue = Time the entity spent waiting to be served. e) What is the proportion of time the server 1 and 2 are idle? Idle time = Time where the server is not servicing an entity, i.e. "not busy" time. d) Burke's theoreml shows that for the MM/1 queue in the steady state with arrivals a Poisson process with rate parameter , the departure process is also a Poisson process with rate parameter . Please compare your simulation outcomes with the

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Statistics and Probablity
Consider a cell-phone repair shop. Customers are arriving to a cell-phone repair shop
with an exponentially distributed inter-arrival time with mean of 5 minutes. Once they
arrive, they are interviewed by a clerk to fill the necessary warranty paperwork. The
clerk's service time is exponentially distributed with mean of 3 minutes. After the
interview the customer waits in an infinite capacity waiting room until the repairman
calls for their number to be served. The repairman total service time is exponentially
distributed with mean of 4 minutes. The customer leaves the building when the
repairman finishes the work and returns the cell phone. In this repair shop there is only
one clerk and one repairman. They can only serve one customer at a time and the
customers are served on a "first-come-first-served" (FCFS) basis. Please construct a
simulation and answer the following questions:
a) What is the average time that a customer spends in the whole system? Time spent
in the system = amount of time that the entity spent in the system from arrival to
departure.
b) What is the average waiting time in queue 1? in queue 2? Time in queue = Time
the entity spent waiting to be served.
c) What is the proportion of time the server 1 and 2 are idle? Idle time = Time where
the server is not servicing an entity, i.e. "not busy" time.
d) Burke's theoreml shows that for the MM/1 queue in the steady state with arivals
a Poisson process with rate parameter À, the departure process is also a Poisson
process with rate parameter . Please compare your simulation outcomes with the
analytical results.
Transcribed Image Text:Statistics and Probablity Consider a cell-phone repair shop. Customers are arriving to a cell-phone repair shop with an exponentially distributed inter-arrival time with mean of 5 minutes. Once they arrive, they are interviewed by a clerk to fill the necessary warranty paperwork. The clerk's service time is exponentially distributed with mean of 3 minutes. After the interview the customer waits in an infinite capacity waiting room until the repairman calls for their number to be served. The repairman total service time is exponentially distributed with mean of 4 minutes. The customer leaves the building when the repairman finishes the work and returns the cell phone. In this repair shop there is only one clerk and one repairman. They can only serve one customer at a time and the customers are served on a "first-come-first-served" (FCFS) basis. Please construct a simulation and answer the following questions: a) What is the average time that a customer spends in the whole system? Time spent in the system = amount of time that the entity spent in the system from arrival to departure. b) What is the average waiting time in queue 1? in queue 2? Time in queue = Time the entity spent waiting to be served. c) What is the proportion of time the server 1 and 2 are idle? Idle time = Time where the server is not servicing an entity, i.e. "not busy" time. d) Burke's theoreml shows that for the MM/1 queue in the steady state with arivals a Poisson process with rate parameter À, the departure process is also a Poisson process with rate parameter . Please compare your simulation outcomes with the analytical results.
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