《Optimization of the CBSMAP Queueing Model》.pdf

JournalofMathematicsandSystemScience3(2013)359-364 OptimizationoftheCBSMAPQueueingModel KondrashovaE．V． DepartmentofHigherMath，NationalResearchUniversityHigherSchoolofEconomics，MoscowStateInstituteofElectronicsand Mathematics，BolshoiTrekhsvyatitelskijper．，3，129347,Moscow，Russia Received：May20，2013／Accepted：June22，2013／Published：July25，2013 Absract：ThepresentpaperisdevotedtotheresearchofcontrolledqueueingmodelsatcontrolofCBSMAP (ControlledBatch Semi-MarkovArrivalProcess)．Thecontrolisbasedonthetheoryofcontrolledsemi-markovprocessesforsystemoptimization．The controliscarriedoutusingatypeofthenextbatchandmomentsofbatcharrivals ． Keywords：Controlledqueuingmodels，optimization，controlledprocess，controlledarriva1．flow 1．IntrOducti0n 尸{+， j,O+，f，+，∈ ／ =f，0= ，u= )： The functioning of different systems can be = P 忤l=j，o f，u ∈ ／ =f}， (1) described using queueing models．To increase the ，u，∈丘 ，r∈R ， ∈ ∈A effi ciencyofthesystem functioningweuseacontro1． = 尸{ =f， 007Uo∈∽ ． Inthepresentpaperaprocessofsystem functioningis Usefollowingdesignations： investigatedatancontrolledarrivalprocess(flow)． P{4+， ，0+ f，“”+，∈B ／ =f}= This controlled process is a generalization of a = (f，B)． (2) BMAP—flow (BatchMarkovArrivalProcess)[1，2]． Foreachstateithesetofcontrols anda-algebra BMAP is good for modeling of data-flows in Aiofsubsetsofthisset isgiven． telecommunicationnetworks． At —÷∞ and B =