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Queuing Theory for Data Networks

Queuing Theory for Data Networks. Queuing Theory for Data Networks. Analysis based on queuing theory enables one to compute the average & standard deviation of queuing time spent in each node, which is the sum of wait and service times as follows: T q = T w + T s

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Queuing Theory for Data Networks

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  1. Queuing Theory for Data Networks

  2. Queuing Theory for Data Networks Analysis based on queuing theory enables one to compute the average & standard deviation of queuing time spent in each node, which is the sum of wait and service times as follows: Tq = Tw + Ts By enumerating all the nodes and queues in path of a message, one can estimate the first two moments of total delay encountered.

  3. Host SNA 1 2 n Controller Terminal Queuing Theory for Data Networks Basic configurations for data networking: A Typical SNA Netlink

  4. Host/SW PS PS PS PS Terminal Queuing Theory for Data Networks Basic Configurations for Data Networking:A FPS Netlink 2 N 1 3

  5. Queuing Theory for Data Networks Basic Configurations for Data Networking: A PS/FPS Backbone: PS PS Netlinks Trunks PS

  6. Communications Protocols for Data • 1: ASYNC Communications Protocol Host WS or a Controller inp. msg out. msg Note:Performance will suffer at high loads due to no control.

  7. Communications Protocols for Data 2:Binary Synchronous Communications (BSC) Protocol as used in SNA : host controller EOT, P host controller I Msg EOT +Poll Ack EOT Select Ack EOT Msg Ack Idle Poll Productive Poll

  8. Queuing Theory for Data Networks Modeling two queues in series in a PS node: Inp. Queue Out. Queue Server Server Inp. Service Out. Service Note: Each PS node has at least two queues in series.

  9. Queuing Theory for Data Networks: M/M/1 Queue Random arrivals, negative exponential service time distribution and 1 server: 1st two moments for time in queue (Tq) are E ( Tq) = E ( Ts ) / (1-) and Std Dev ( Tq) = E ( Ts ) / (1-) where is server utilization , E( Ts ) is the avg. service time, Tq is the time in queue =time to wait plus time to be serviced.

  10. Queuing Theory for Data Networks: M/D/1 Queue Random Arrivals, constant service time distribution and 1 server: 1st two moments for time in queue ( Tq) are as follows: E ( Tq) = [Ts (2- /[2 (1-)] and Std Dev ( Tq)=[Ts / (1 -)] [SQR(/3-/12)] where Ts is the service time and is the utilization of the server.

  11. M/M/1 & M/D/1 Queuing Delays E ( Ts)*10 m s M/M/1 Legend: m= E(Tq) s=std.dev. =media utiliztion s m 5 E ( Tq) & Std.Dev. M/D/1 0  0 1.0

  12. Queuing Theory for Data Networks: M/M/N Queue Prob (delay > T) = Po * Exp [-(N-A)T/ Ts] where Ts = expected service time = E ( Ts ) Po= Prob. (delay > 0.0) = (B*N) / [N-A(1-B)] B=ErlB blocking for A erlangs and N servers

  13. Queuing Theory for Data Networks: M/M/N Queue E (Tw) = avg. time in waiting = Ts / (N-A) for delayed transactions =Ts * Po/(N-A) for all transactions and Std. Dev.(Tq)= [Ts/(N-A)]*SQR[Po(2-Po)+ (N-A)2] where Po, N, Ts and A have been defined earlier.

  14. Queuing Theory for Data Networks: M/D/N Queue Prob (Delay > T) = Po*Exp[-2*(N-A)T/Ts] The 1st two normalized moments are: AVG( Tq) = 1 + [Po/2(N-A)] VAR(Tq) = [1/(N-A)2 ]*[ Po/3 - (Po)2 /12 ] Po ­ Po, 0.98Po & .94Po(N = 1, 2, >2..M/M/N) See TEXT-Appendix A for exact equations and some useful plots of Po for some useful values of N servers and A erlangs.

  15. M/M/N & M/D/N Queues Prob (delay > T)  1.0 Legend: 0.67 M/M/N . 5 M/D/N See TEXT for more data. N=1 N=3 0 4 5 2 3 0 1 Delay =T / Ts

  16. Queuing Theory for Data:End-to-End Delays The Avg. and Variance of end-to-end delay in a data network can be expressed as : Avg. (Tqs) = Avg. (Tqi)... (is sum over i) Var. (Tqs) =  Var (Tqi) = [Std.Dev.(Tqs)]2 Also we have: Tqs(90%)=Avg.(Tqs)+1.28 SQR[Var. (Tqs)] Tqs(95%)=Avg.(Tqs)+1.65 SQR[Var. (Tqs)] Tqs(99%)=Avg.(Tqs)+2.33 SQR[Var. (Tqs)]

  17. Class Assignments 1. Review M/M/1 and M/D/1 queue by plotting AVG( Delay) Versus  2. Compute and plot the ratio of two AVG(Delay) values Versus 

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