1 / 7

Chapter 18: Queuing Models

Chapter 18: Queuing Models. C*. Capacity decisions: a trade-off . Total cost. Cost of Service (provider). Cost . Cost of Waiting (customer). Capacity to serve. Model Nomenclature & Terms . A/B/C = arrival dist / service dist / # of servers Poisson arrivals (M)

Samuel
Download Presentation

Chapter 18: Queuing Models

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 18: Queuing Models

  2. C* Capacity decisions: a trade-off Total cost Cost of Service (provider) Cost Cost of Waiting (customer) Capacity to serve

  3. Model Nomenclature & Terms • A/B/C = arrival dist/ service dist/ # of servers • Poisson arrivals (M) • Distribution of independent arrivals over time • Exponential service (M) (time between poisson arrivals) • General service (G) (other distributions)

  4. M/M/1 Customers waiting Customer being served • λ = average customer arrivals per hour • μ = average service rate per hour λ μ Lq = length of queue Ls =length of (# of customers in) system

  5. M/M/1 λ μ-λ Length in System (Ls) = 1 μ-λ Time in System (Ws) = In an effort to maximize efficiency, the manager of the airport tried to get the average time per take off to equal the time between arrivals. What will happen?

  6. Definitions • n = number of customers in the system • ρ = mean number of customers in system (λ/μ) • N = maximum number of customers in system • c = number of servers • Pn = probability of exactly n customers in system • L = number of customers in (s=system,q=queue, b=busy system) • W= mean waiting time of a customer in (s=system,q=queue, b=busy system)

  7. let’s try one

More Related