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

International trade, why does south africa regulate int''l trade

why does south africa regulate int''l trade

Quality circles, advantage of quality circle process

advantage of quality circle process

Steps of research proposal, Steps of Research Proposal Proposal Con...

Steps of Research Proposal Proposal Content  The researcher is always given instructions for preparing a proposal that indicate the format to be followed. Funding agencie

Institutional Characteristics - information resources, Institutional Charac...

Institutional Characteristics:  An approach to an understanding of the fields of interest of individuals to be served and of the organisation as a whole could begin by acquiri

On the basis of ratio of change direction, On the  Basis  of Ratio of Ch...

On the  Basis  of Ratio of Change  Direction   a. Linear Correlation: The  correlation  between  two variables a said  to be liner if  corresponding  to a unit change in th

Software, role of computer software in operation research

role of computer software in operation research

Vam, how to solve it

how to solve it

Question, i need many good and important question of operation research obo...

i need many good and important question of operation research obout dinamic programing and non-liner programing and integer orograming ....for study! thank you

Nass food produce tow kinds of popular dark chocolate bars, Nass food prod...

Nass food produce tow kinds of popular dark chocolate bars

Necessity of operations research, After having studied as to what is op...

After having studied as to what is operations research we shall now try to answers why its need has been felt by the industry. As already tainted out science of OR came

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