Data Networks Solutions

 Documents

 2 views
of 105
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Description
SOLUTIONS MANUAL Second Edition Data Networks DIMITRI BERTSEKAS Massachusetts Institute a/Technology ROBERT GALLAGER Massachusetts Institute a/Technology II PRENTICE HALL. Englewood Cliffs. New Jersey 07632 ã © 1993 by PRENTICE-HALL, INC. A Paramount Communications Company Englewood Cliffs. New Jersey 07632 All rights reserved 10 9 8 7 6 5 4 3 ISBN 0-13-200924-2 Printed in the United States of America CHAPTER 3 SOLUTIONS 3.1 A customer that carries out the order (eats in the
Share
Tags
Transcript
  SOLUTIONSMANUAL SecondEdition Data Networks DIMITRI BERTSEKAS MassachusettsInstitutea/Technology ROBERT GALLAGER MassachusettsInstitutea/Technology II PRENTICEHALL. EnglewoodCliffs.NewJersey07632  ã 1993 by PRENTICE-HALL,INC.AParamountCommunicationsCompanyEnglewoodCliffs.NewJersey07632Allrightsreserved 109876543 ISBN 0-13-200924-2 Printed in theUnitedStates of America  CHAPTER3SOLUTIONS 3.1 Acustomerthatcarriesouttheorder(eatsin the restaurant)staysfor5mins (25mins). Thereforetheaveragecustomertime in thesystemisT=0.5*5 + 0.5*25= 15. By Little'sTheoremtheaveragenumber in thesystemisN= A*T = 5*15=75. 3.2 Werepresentthesystemasshown in the figure. Thenumber of fl1es in theentiresystem is exactly one at all times.Theaveragenumber in nodeiis AiRi and theaveragenumber in node3is'IolPl + A2P2. Thereforethethroughputpairs (AhA2) mustsatisfy (in addition to nonnegativity)theconstraint If the systemwereslightlydifferent and queueingwereallowed at node 3, while nodes1and2couldtransmitatwill,adifferentanalysiswouldapply.Thetransmissionbottleneckforthefiles of node 1impliesthat 1 A S- } R} Similarlyfornode2 we get that Node3 can work on onlyonefileatatime. If we lookatthefllereceivingserviceatnode3asasystemandletNbetheaveragenumberreceivingserviceatnode3, we conclude from Little'stheoremthat  and NS1 This impliesthat AIPI+A 2 P 2 S1 3.3 Working Machines ... -. R Machines . Waiting Repair Q Repairmen We representthesystem as showninthefigure. In particular,onceamachine breaks down, it goesintorepair if arepairperson is available at thetime,andotherwisewaitsinaqueue for arepaiIpersontobecomefree.Notethat if m= 1 thissystemisidentical to theone of Example3.7.Let A be thethroughput of thesystemandlet Q be theaveragetimeabrokendownmachinewaitsforarepairperson to become free. ApplyingLittle'stheorem to theentiresystem,weobtain A(R+Q+P) =N fromwhich A(R+P) SN (1) (2) Sincethenumber of machineswaitingrepair canbe atmost (N-m), theaveragewaitingtime AQ is at mosttheaveragetimetorepair(N-m)machines,whichis(N-m)P.Thus,fromEq. (1) weobtain A(R+ (N - m)P +P) ~ N ApplyingLittle'stheoremtotherepairpersons,weobtain APSm (3) (4)
Related Search
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks