The following assumptions are made for this model
Model 2 : (M/M/C) : (GD/ ∞/ ∞ ) Model
The
following assumptions are made for this model:
The
arrival rate follows Poisson distribution
The
service rate follows Poisson distribution
The
number of servers is C
The
service discipline is general discipline
The maximum number of customers allowed in the
system is infinite
With these assumptions, the steady state equation for the probability of
having n customers in the system is given by
Example 1
At a Toll Gate, vehicles arrive
at the rate of 24 per hour and the arrival rate follows Poisson distribution.
The time to collect a toll and permitting the vehicle to pass follows
exponential distribution and the passing rate is 18 vehicles per hour. There
are 4 passing counters. Determine the following:
1. Po and P3
2. Lq, Ls,
Wq and Ws
Solution
The
arrival rate δ= 24 per hour.
The
passing rate µ = 18 Per hour.
No. of
passing counters C=4.
Example 2
In a bank, there are two cashiers
in the cash counters. The service time for each customer is exponential with
mean 4 minutes and the arrival rate of the customers is 10 per hour and the
arrival of the customers follows Poisson distribution. Determine the following:
1. The
probability of having to wait for service
2. The
expected percentage of idle time for each cashier
3.
Whenever a customer has to wait,
how much time he is expected to wait in the Bank?
Solution
Tags : Operations Management - Game Theory, Goal Programming & Queuing Theory
Last 30 days 1985 views