Consider an M/M/1 queue in which the expected number of customers in the system is 4, and the expected waiting time in the system is 80 minutes. What is the probability that a customer’s service time is less than 40 minutes?

Step-by-step explanation:

Given

Expected no of customer in the system is 4 i.e. length of queue is

Expected waiting time in the system

Length of queue is given by

thus

where

L is also given by

therefore

where =mean arrival rate

=mean service rate

Probability that customer service rate is less than 40 minutes is

3100

step-by-step explanation:

answer: the proof is mentioned below.

step-by-step explanation:

since, given:   lines bc = ef

prove:   lines ac > ef

          statements                                           reason

1. bc=ef                                           1. given

2. ac= ab+bc                                 2. because b is the point between the  

                                                            line segment ac

3.   ac > bc                                       3. because if a line segment is equal to

                                                          the sum of two line segments then it is

                                                          always greater then each of these

                                                          individual line segments

4. ac > ef                                         4. by equality property.