1. Consider a single-line, single-server waiting line system. Suppose that there
ID: 403599 • Letter: 1
Question
1. Consider a single-line, single-server waiting line system. Suppose that there is only physical space for 2 units in the system (one in line and one being served). The arrival rate %u03BB is 80 people per hour. The manager, Johnny Three Toes, has the choice among workers of different speeds to be the server. He wants to save money by hiring the slowest server that will result in an average number of units in the system (L) equal to 2.
a) Using Johnny Three Toes%u2019 strategy, what will the server%u2019s service rate per hour (%u03BC) need to be?
b) What is the probability of having 3 or more units in the system?
c) What is wrong with Johnny Three Toes%u2019 strategy?
please with calculation
Explanation / Answer
b)
probability that there are 'n' customers in the system
P(L=n) = (1-p) * p^n
probability of having more than 3 customers in the system
= P(L>=3)
= 1 - [ P(L=0) + P(L=1) + P(L=2) ]
= 1 - [0.3333+0.2222+0.1481]
=0.2964
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