Discrete-time buffer systems with session-based arrival streams

Abstract

The paper considers a discrete-time buffer system with infinite storage capacity and one single output channel. Users can start and end sessions during which they are active and send packets to the buffer system. In this paper we study a simple model for the resulting session-based arrival process: we assume that each active user generates a random but strictly positive number of packets per time slot. Furthermore it is assumed that the time (expressed in slots) needed to transmit a packet is geometrically distributed. The distribution of the session lengths is also geometrical. This model can be applied to study the traffic of a file server, where one file download by a user is considered to be one session. The probability generating functions of the steady-state number of active sessions, the buffer occupancy and the packet delay are derived. We also derive an approximation for the tail probabilities of the buffer occupancy. Furthermore, an expression for the mean session delay is obtained. This allows us to study the influence of the different system parameters: some examples are presented. We end by applying the model to a web server, based on actual web traffic.

Discrete-Time Buffer Systems With Session-Based Arrivals and Markovian Output Interruptions

“…Hoflack et al [5] and Wittevrongel et al [1] investigated the session-based arrival models with multiple session types and one output line. In [5] the session lengths and the transmission times of the packets are geometrically distributed.…”

“…Hoflack et al [5] and Wittevrongel et al [1] investigated the session-based arrival models with multiple session types and one output line. In [5] the session lengths and the transmission times of the packets are geometrically distributed. But in [1] the session lengths are generally distributed and the output line is unreliable and prone to stochastic failures, where the effective transmission times (that are required for the successful transmission of a packet) are geometrically distributed.…”

A Taylor series expansions approach to queues with train arrivals

“…It is well known that input correlation significantly affects queueing performance and hence there is a continuing interest in analytically tractable queueing models which can accurately capture arrival correlation. There is a particular interest in Markovian arrival models, including models with a finite state space such as the discrete-time batchMarkovian arrival model [1,2], or with a structured infinite state space such as the discrete autoregressive arrival models [3,4], branching arrival models [5] and train arrival models [6,7,8,16].…”

Session Delay in File Server Output Buffers with General Session Lengths

“…The session-based arrival process was proposed in [1] and [2] to model the outgoing data buffer behavior of a web server, where a geometric distribution was assumed for the session lengths. It has been observed however that files on file and web servers are typically either small or very large and the file-size distribution is heavy-tailed, see e.g.…”