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Operations Management - Game Theory, Goal Programming & Queuing Theory

Model 2 : (M/M/C) : (GD/ ∞/ ∞ ) Model - Types of Waiting Line Models - Queueing Theory

   Posted On :  25.06.2018 02:43 am

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
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