" />  M/M/N Queuing - Essay Writing Pros

M/M/N Queuing

M/M/N Queuing A more general formulation of the M/M/1 queue is the M/M/N queue, where N is the total number of departure channels. M/M/N queuing is a reasonable assumption at toll booths on turnpikes or at toll bridges, where there is often more than one departure channel available (more than one toll booth open). A parking lot is another example, with N being the number of parking stalls in the lot and the departure rate, μ, being the exponentially distributed times of parking duration. M/M/N queuing is also frequently encountered in non- transportation applications such as checkout lines at retail stores, security checks at airports, and so on.

The following equations describe the operational characteristics of M/M/N queuing. Note that unlike the equations for M/D/1 and M/M/1, which require that the traffic intensity, ρ, be less than 1, the following equations allow ρ to be greater than 1 but apply only when ρ/N (which is called the utilization factor) is less than 1.

Don't use plagiarized sources. Get Your Custom Essay on
M/M/N Queuing
Just from \$13/Page

( ) ρ ρρ

−== +

− 0 101

! ! 1cc

N n N

cnP

n N N

(5.34)

0 for !

nnP P n N

n ρ

= ≤ (5.35)

5.5 Queuing Theory and Traffic Flow Analysis 179

ρ−= ≥0 for !

nn n N

P P n N

N N (5.36)

( ) 10! 1

Nn NP P

N N N ρ

ρ

+> = −(5.37)

where

P0 = probability of having no vehicles in the system, Pn = probability of having n vehicles in the system,

Pn>N = probability of waiting in a queue (the probability that the number of vehicles in the system is greater than the number of departure channels),

n = number of vehicles in the system, N = number of departure channels, nc = departure channel number, and

ρ = traffic intensity (λ/μ).

Calculate your paper price
Pages (550 words)
Approximate price: -

Why Work with Us

Top Quality and Well-Researched Papers

Our writers have been trained on how to handle papers placed by our clients. The writer must read and understand before embarking on writing the papers. In case of any issue that needs clarification, writers are encouraged to ask the client or support.

Professional and Experienced Academic Writers

Our team comprises of the best writers and editors. We do thorough vetting during recruitment to make sure that our writers have the knowledge and experience we aspire in the team.

Free Unlimited Revisions

Our aim is to give the client the best outcome. If for some reason you are not satisfied with the wok done, you can ask the paper to be revised or rewritten. This will be done to your satisfaction with no extra charges.

Prompt Delivery and 100% Money-Back-Guarantee

We have writers who work round the clock. This helps in making sure that all our clients’ papers are delivered on time. If we have issues with the deadline, we will ask for extension. If its not possible, the money is fully refunded.

Original & Confidential

Our clients’ confidentiality is highly respected. We can never disclose our clients’ details to third parties. In the same regard, we strive to give our clients 100% original papers. We do not tolerate plagiarism from our writers.

Clients can reach us any time of the day, and any day of the week. There is a live chat, email or phone numbers to help in ease of communication.

Try it now!

Calculate the price of your order

Total price:
\$0.00

How it works?

Follow these simple steps to get your paper done

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

You should never be worried about your papers even in the middle of the night. Our team will work round the clock to deliver.

Essay Writing Service

We have an able team that can deliver your work in the shortest time possible. The academic level or the type of work should never be a hindrance. Our highly competent support team is always around (24/7) to give you any assistance you may need.

Do you need to be admitted in your dream institution but find it challenging to write an admission essay? Our team is in a position to write the best letter that will guarantee you an admission. We do as well write the best business proposals and reports.

Editing Support

Writing can be fun and enjoyable when everything has been done right. Writing is not just enough without proper editing and proofreading. We have a team of editors that ensure everything falls in place, whether its issues to do with grammar or referencing styles.

Revision Support

Once the paper has been done and submitted, that is not the end of it. You can always ask for amendment or improvement if you feel something has not been done right. Our team of writers and editors will gladly assist you to your satisfaction. Revision is free of charge.