Traffic processes in queueing networks: a Markov renewal approach
Traffic processes in queueing networks: a Markov renewal approach
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Discrete-Time Models for Communication Systems Including ATM
Discrete-Time Models for Communication Systems Including ATM
The response time distribution of a discrete-time queue under a generalized batch arrival process
LANC '05 Proceedings of the 3rd international IFIP/ACM Latin American conference on Networking
Performance evaluation of multichannel Slotted-ALOHA networks with buffering
ICN'05 Proceedings of the 4th international conference on Networking - Volume Part II
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In this paper, an exact solution for the response time distribution of a single server, infinite capacity, discrete-time queue is presented. This queue is fed by a flexible discrete-time arrival process, which follows an on/off evolution. A workload variable is associated with each arrival instant, which may correspond to the service demand generated by a single arrival, or represent the number of simultaneous arrivals (bulk arrivals). Accordingly, the analysis focuses on two types of queues: (On/Off)/G/1 and (Batch-On/Off)/D/1. For both cases, a decomposition approach is carried out, which divides the problem into two contributions: the response time experienced by single bursts in isolation, and the increase on the response time caused by the unfinished work that propagates from burst to burst. Particularly, the solution for the unfinished work is derived from a Wiener-Hopf factorization of random walks, which was already used in the analysis of discrete GI/G/1 queues. Compared to other related works, the procedure proposed in this paper is exact, valid for any traffic intensity and has no constraints on the distributions of the input random variables characterizing the process: duration of on and off periods, and workload. From the general solution, an efficient and robust iterative algorithm for computing the expected response time of both queues is developed, which can provide results at any desired precision. This algorithm is numerically evaluated for different types of input distributions and proved against simulation.