1 / 18

Queuing Analysis

Queuing Analysis. COMT 429. Call/Packet Arrival. Arrival Rate,  Inter-arrival Time, 1/  Arrival Rate measures the number of customer arrivals per time unit, e.g Calls per hour Packets per second. “Call Length”. Service Time, s Service Rate,  =1/s

linus-barry
Télécharger la présentation

Queuing Analysis

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. Queuing Analysis COMT 429

  2. Call/Packet Arrival • Arrival Rate,  • Inter-arrival Time, 1/ • Arrival Rate measures the number of customer arrivals per time unit, e.g • Calls per hour • Packets per second

  3. “Call Length” • Service Time, s • Service Rate, =1/s • In circuit switched networks, the service time is the average call length.

  4.  =  Utilization • Measures the Arrival Rate relative to the Service Rate • The queue becomes congested if the utilization is larger than the number of servers  = s * 

  5. “Poisson Arrival” • Describes random call or packet arrival • Measured over a short time, the probability of call arrival is proportional to , the arrival rate • Over long times, the probabilities of x call arrivals follow the Poisson Distribution

  6. “Exponential Service Time” • Despite the different name, this assumption means that calls “leave” the system as randomly as they entered. • It assumes that services times are random, and not related from call to call

  7. Queue Type: Kendall Notation • Arrival/Service/#Servers/Queue Slots • M/M/n or M/M/n/∞ • Poisson Arrival, Exponential Services time, n Servers • M/G/n • General services times • M/D/n • Fixed (Deterministic) service times

  8. Queueing in Circuit Switching • Remember that Utilization is defined as the (Service Time) * (Calls/Time Unit) • Service Time in a circuit switching environment is identical to call length • Utilization is therefore the same as our definition of total traffic (in Erlangs)

  9. Multi-Server Call Queue Queue “a” Erlangs of Traffic “c” circuits aka servers This system is only stable for “a” less than “c”

  10. Erlang C (M/M/c) • Recall that the blocking probability for “a” Erlangs offered on “c” circuits is given by Erlang-B: E’(c,a) • The probabilty of delay is Erlang-C In Erlang C Tables, delay is given in units of h, not including the service time

  11. Systems with Queuing and Blocking • M/M/c/K Queues • “c” servers in the system • Only “K” calls can be active in the system

  12. Queuing Analysis for Data Traffic COMT 429

  13. Service Time for Data Traffic • In packet networks, the service time is computed from the packet length and the bit rate of the circuit. Buffer C bits/sec circuit speed  packets/sec L bits/packet L sec/message Service Time s = C

  14. Summary Buffer C bits/sec circuit speed  messages/sec L bits/message L sec/message Service Time s = C Service Rate  = 1 / s messages/sec  Utilization  = 

  15. Queuing FormulaM/M/1 Queue  messages queued Average Queue Length E(n) = 1 - 

  16. Queue DelayM/M/1 Queue s Including the service time for the call or packet Average Delay E(T) = 1 -  In general, E(T) *  = E(n), the queue delay times the arrival rate equals the queue length

  17. Delay ExampleM/M/1 200 characters/message 8 bits per character 9600 bits/sec line

  18. M/D/1 Queue results   messages queued Average Queue Length E(n) = (1 -  s Including the service time for the call or packet  Average Delay E(T) = (1 - 

More Related