1 / 15

Multiple class queueing networks Mean Value Analysis

Multiple class queueing networks Mean Value Analysis. Open queueing networks - Closed queueing networks. outgoing requests. incoming requests. CPU. DISK. DISK. CD. CD. M clients. CPU. Open queueing network. Closed queueing network (number finite of users). Incoming request class.

mitchellmartha
Download Presentation

Multiple class queueing networks Mean Value 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. Multiple class queueing networksMean Value Analysis • Open queueing networks- Closed queueing networks

  2. outgoing requests incoming requests CPU DISK DISK CD CD M clients CPU Open queueing network Closed queueing network (number finite of users)

  3. Incoming request class Different kind of requests should be in a system (queueing network) that need different services by the servers, i.e: • a database server is subject to two type of transactions: • simple query (that needs only read activities on the disks) • updating transactions (that needs read and write activities on the disks) • a web server is subject to two type of requests: • Read of a little file • Uploading of a big file

  4. Definitions K: number of queues i: queue identification r: class identification (from 1 to R) lr: arrival rate for class r request l = (l1, l2 , ..., lR) Vi,r: average number of visits a class r request makes to server i from its generation to its service time (request goes out from the system if open network) 4

  5. Definitions Si,r: average class r request service time at the server i Wi,r: average class r request waiting time in the queue i Ri,r: average class r request answer time in the queue i Ri,r = Si,r + Wi,r

  6. Definitions R’i,r: average class r request residence time in the queue i from its creation to its service completion time (request goes out from the system in case of open network) R’i,r =Vi,r Ri,r Di,r: request class r service demand to a server in a queue i from its creation to its service completion time (request goes out from the system in case of open network) Di,r =Vi,r Si,r

  7. Formulas for multiple class open QNs Input parameters Di,r , r Equations . Ui,r () = r Vi,r Si,r = r Di,r . Ui () = Rr=1 Ui,r () total utilization factor . R’i,r () = Di,r delaying resource R’i,r () = Di,r / (1-Ui ()) queuing resource

  8. Formulas for multiple class open QNs . R0,r () = Ki=1 R’i,r () . ni,r () = Ui,r () / (1-Ui ()) NOTE: total utilization in the denominator . ni, () = Rr=1 ni,r ()

  9. DISK2 DISK1 CPU DB Server(example ) Class 1 trx: query l1= 5 requests per second (tps) DCPU = 0,1 sec Service demand at CPU DDISK1 = 0.08 Service demand at disk 1 DDISK2 = 0.07 Service demand at disk 2 Class 1 trx: updating trx l1= 2 requests per second (tps) DCPU = 0,15 sec Service demand at CPU DDISK1 = 0.20 Service demand at disk 1 DDISK2 = 0.10 Service demand at disk 2

  10. DISK2 DISK1 CPU DB Server(example )

  11. DISK TAPE M clients CPU Multiclass closed queue networks (finite number of users) 12

  12. Notations Nr: fixed number of requests in the system for each class (r) N: (N1, N2, . . ., NR) 1r: vector where all components are zero except for the r-th component, which is equal to 1

  13. Formulas -> Residence Time Equation for class r R’i,r(N)= Di,r[1+ni(N – 1r)] -> Throughput equation for class r X0,r = Nr / Kr=1 R’i,r(N) -> Queue lenght equation for class r ni,r(N) = X0,r(N) R’i,r -> Queue equation ni(N)= Rr=1 ni,r(N)

  14. Example with 2 classes • Residence Time Equation for class r • R’i,r(N)= Di,r[1+ni(N – 1r)] • for example, to evaluate the formulas, when the state is N=(3,4), i.e. 3 customers of class 1 and 4 customers of class 2, we need to know: • the average number of users in queue i when there are 2 customers of class 1 and 4 customer of class 2 • the average number of users in queue i when there are 3 customers of class 1 and 4 customer of class 3 • R’i,1(3,4)= Di,r[1+ni(2,4)] • R’i,2(3,4)= Di,r[1+ni(3,3)]

More Related