The students patiently form a single line in front of the desk to wait for help

Question

The students patiently form a single line in front of the desk to wait for help at University. Student arrivals are best described by Poisson distribution with mean of 15 students per hour arriving at the help desk. The help desk server can help an average one student in 3 minutes, with the service rate being described by an exponential distribution. Calculate the following characteristics of the service system: (a) The average number of students in the system. (b) The average number of students waiting in the line. (c) Probability that no student is in the system.

Explanation / Answer

Given, mean arrival rate, = 15 students per hour, mean service rate, =20 students per hour(3minutes 1 student)

The average utilization of the help desk server, p = / = 15/20 = 0.75 or 75%

(a) The average number of students in the system, L= /(-) = 15/(20-15 = 3 students

(b) The average number of students waiting in line, LQ =pL = 0.75*3 = 2.25 students. This is approximately3 students

p=p(1-p) power n it gives probability of n customers in a system

c) probability of no student in system , n=0

p=0.75

p(0)=0.75(1-0.75) power o

=0.75*1

=0.75

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