Question
In: Statistics and Probability
Customers arrive at a two-server system according to a Poisson process having rate λ = 5....
Customers arrive at a two-server system according to a Poisson
process having rate λ = 5. An arrival finding server 1 free will
begin service with that server. An arrival finding server 1 busy
and server 2 free will enter service with server 2. An arrival
finding both servers busy goes away. Once a customer is served by
either server, he departs the system. The service times at server i
are exponential with rates μi, where μ1 = 4, μ2 = 2.
(a)
Find the long-run proportion of time that there is only one
customer in the system.
(b)
What proportion of time is server 2 busy?
(c)
What is the average time an entering customer spends in the
system?
Solutions
orchestra answered 2 years agoRelated Solutions
Customers arrive at a two-server system at a Poisson rate λ=5. An arrival finding the system...
Customers arrive at a two-server system at a Poisson rate λ=5.
An arrival finding the system empty is equally likely to enter
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system will enter service with the idle server. An arrival finding
two others will wait in line for the first free server. The
capacity of the system is 3. All service times are exponential with
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A queueing system serves two types of customers. Type 1 customers arrive according to a Poisson...
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system has two servers, both of which serve both types of customer.
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minutes. Service is provided on a first-come-first-served
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