Page 227 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes 3. Average interval between successive intervals is 0.2 hour.

Average arrival rate, l = = 5 arrivals per hour.

Average Inter-arrival time, = 0.2 hour.
Similarly, in the following service situations, the average service rate per hour, µ and average
service time in hours are determined.
1. One service is completed in 10 minutes.

Average service rate, m = = 6 services per hour.

Average service time, = = 10 minutes or 0.166 hour.
2. Number of customers served in 15 minutes is 4.

Average service rate, m = × 60 =16 services per hour.

Average services time, = = 3.75 mins or 0.0625 hour.
3. Average service time is 0.25 hour.
Average service rate, m = 4 services per hour.

Average service time = 15 mins or 0.25 hour.

Example: In a factory, the machines break down and require service according to a
Poisson distribution at the average of four per day. What is the probability that exactly six
machines break down in two days?
Solution:
Given  = 4, n = 6, t =2

P(n, t) = P(6, 4) when l = 4
  

we know, P(n, t) =

   
P(6,2) =

=
= 0.1221

Example: On an average, 6 customers arrive in a coffee shop per hour. Determine the
probability that exactly 3 customers will reach in a 30 minute period, assuming that the arrivals
follow Poisson distribution.

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