Describe states-transitions and transition rate, Operation Research

Customers arrive to a super market according to a Poisson process with intensity V = ½  per minute. The supermarket has two counters, that use a common queue. Counter 1 is always occupied. Counter 2 is opened when 3 or more customers are in the queue, and will be closed when the counter becomes idle (no customer is served at counter 2). The service time of a customer has an exponential distribution with mean 1/W = 1 minute.

a)      Draw the transition diagram for this queueing system. Describe the states, transitions, and transition rates. Hint: define the states (i, j) with i the number of customers, j the number of counters in use.

b)      Give the equilibrium equations.

You do not have to solve the equilibrium equations in b). The following questions must be answered in terms of the arrival intensities  V, the average service time 1/W, and the equilibrium probabilities P(i,j).

c)      Give the average number of customers in the queue.

d)     Give the average waiting time per customer.

e)      How many counters are open on average?

f)       Which percentage of time all counters are occupied?

g)      What is the fraction of time counter 2 is occupied?

h)      Determine the average length of a period during which counter 1 is not occupied.

Posted Date: 3/5/2013 8:12:13 AM | Location : United States







Related Discussions:- Describe states-transitions and transition rate, Assignment Help, Ask Question on Describe states-transitions and transition rate, Get Answer, Expert's Help, Describe states-transitions and transition rate Discussions

Write discussion on Describe states-transitions and transition rate
Your posts are moderated
Related Questions
Maximize Z =3x+4x subject to x1+x2 =3 2x1+3x2 =4 x1,x2 =0

regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual

Cost The  cost factor  is a very  important  factor in determining  the size of the  sample. The budget for research should be properly  decided. The management may not lik

I''m getting a negative value in the one of the Supply/Stock columns while solving a problem in Vogel''s approximation method. Is it possible or am I doing anything wrong?

Solve the following Linear Programming Problem using Simplex method. Maximize Z= 3x1 + 2X2 Subject to the constraints: X1+ X2 = 4 X1 - X2 = 2 X1, X2 = 0

A paper mill produces two grades of paper viz X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper in

A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i

Normal 0 false false false EN-IN X-NONE X-NONE PROBABILITY DISTRIBUTION

what skill use by maybacnk CEO

A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i