One hundred employees of a company are asked how they get to work and whether they work full time or part time. The table below
2 answers:
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Answer:
a) and that represent the 33%
b)
c)
d)
e)
f)
Step-by-step explanation:
Notation
P represent the probability that the employee is idle
represent the probability that the employee is busy
represent the average number of people receiving and waiting to receive some information
represent the average number of people waiting in line to get some information
represent the average time a person seeking information spends in the system
represent the expected time a person spends just waiting in line to have a question answered
This an special case of Single channel model
Single Channel Queuing Model. "That division of service channels happen in regards to number of servers that are present at each of the queues that are formed. Poisson distribution determines the number of arrivals on a per unit time basis, where mean arrival rate is denoted by λ".
Part a
Find the probability that the employee is idle
The probability on this case is given by:
In order to find the mean we can do this:
And in order to find the probability we can do this:
and that represent the 33%
Part b
Find the proportion of the time that the employee is busy
This proportion is given by:
Part c
Find the average number of people receiving and waiting to receive some information
In order to find this average we can use this formula:
And replacing we got:
Part d
Find the average number of people waiting in line to get some information.
For the number of people wiating we can us ethe following formula"
And replacing we got this:
Part e
Find the average time a person seeking information spends in the system
For this average we can use the following formula:
Part f
Find the expected time a person spends just waiting in line to have a question answered (time in the queue).
For this case the waiting time to answer a question we can use this formula: