Describe states-transitions and transition rate, Operation Research

Assignment Help:

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.


Related Discussions:- Describe states-transitions and transition rate

Uses of mean deviation - measure of dispersion, Uses  of Mean  Deviation...

Uses  of Mean  Deviation Mean  Deviation  is rarely being used as a measure of dispersion. But  due to  easy  and  simplicity  in calculation. It  is rather  useful  in busin

CONCEPT OF DUALITY IN LPP, EXPLAIN THE CONCEPT OF DUALITY IN LPP THROUGH A ...

EXPLAIN THE CONCEPT OF DUALITY IN LPP THROUGH A LIFE SITUATION

Regression Analysis, regression line drawn as Y=C+1075x, when x was 2, and ...

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

Answering lp problems, ABC Company manufactures both interior and exterior ...

ABC Company manufactures both interior and exterior paints from 2 raw materials M1 and M2. The following table gives basic data of problem.     Exterior

Research process and methodology , Case Study - Research Process Tomz...

Case Study - Research Process Tomzak  and Hale  inc was a medium sized  marketing  research firm  located  in a large mind western  city. Bob Lynn a marketing  vice president

Operation research, A paper mill produces two grades of paper viz., X and Y...

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

Linear Programming, b. A paper mill produces two grades of paper viz., X an...

b. 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 pape

Method of calculation of mean deviation, Method of Calculation of Mean  De...

Method of Calculation of Mean  Deviation a. Computation of Mean Deviation Individual Series : The process of computing mean  deviation in case  of individual series involves

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd