This paper considers the Geom/G/1 queueing model with feedback according to a latearrival system with delayed access (LASDA).Using recursive method,this paper studies the transientproperty of the queue size from the i...This paper considers the Geom/G/1 queueing model with feedback according to a latearrival system with delayed access (LASDA).Using recursive method,this paper studies the transientproperty of the queue size from the initial state N(0^+)=i.Some new results about the recursiveexpression of the transient queue size distribution at any epoch n^+ and the recursive formulae of theequilibrium distribution are obtained.Furthermore,the recursive formulae of the equilibrium queuesize distribution at epoch n,and n are obtained,too.The important relations between stationaryqueue size distributions at different epochs are discovered (being different from the relations given inM/G/1 queueing system).The model discussed in this paper can be widely applied in all kinds ofcommunications and computer network.展开更多
In this paper, the Geometry/G/1 queueing model with inter-arrival times generated by a geometric（parameter p） distribution according to a late arrival system with delayed access and service times independently distr...In this paper, the Geometry/G/1 queueing model with inter-arrival times generated by a geometric（parameter p） distribution according to a late arrival system with delayed access and service times independently distributed with distribution {gj }, j≥ 1 is studied. By a simple method （techniques of probability decomposition, renewal process theory） that is different from the techniques used by Hunter（1983）, the transient property of the queue with initial state i（i ≥ 0） is discussed. The recursion expression for u -transform of transient queue-length distribution at any time point n^＋ is obtained, and the recursion expression of the limiting queue length distribution is also obtained.展开更多
基金supported by the National Natural Science Foundation of China under Grant No. 70871084the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No 200806360001the Scientific Research Fund of Southwestern University of Finance and Economics
文摘This paper considers the Geom/G/1 queueing model with feedback according to a latearrival system with delayed access (LASDA).Using recursive method,this paper studies the transientproperty of the queue size from the initial state N(0^+)=i.Some new results about the recursiveexpression of the transient queue size distribution at any epoch n^+ and the recursive formulae of theequilibrium distribution are obtained.Furthermore,the recursive formulae of the equilibrium queuesize distribution at epoch n,and n are obtained,too.The important relations between stationaryqueue size distributions at different epochs are discovered (being different from the relations given inM/G/1 queueing system).The model discussed in this paper can be widely applied in all kinds ofcommunications and computer network.
基金This work was supported by the Scientific Research Fund of Southwestern University of Finance and Economics and the Science Foundation of Sichuan Normal University.
文摘In this paper, the Geometry/G/1 queueing model with inter-arrival times generated by a geometric（parameter p） distribution according to a late arrival system with delayed access and service times independently distributed with distribution {gj }, j≥ 1 is studied. By a simple method （techniques of probability decomposition, renewal process theory） that is different from the techniques used by Hunter（1983）, the transient property of the queue with initial state i（i ≥ 0） is discussed. The recursion expression for u -transform of transient queue-length distribution at any time point n^＋ is obtained, and the recursion expression of the limiting queue length distribution is also obtained.
