Analysis of a random-access protocol under long-range-dependent traffic

Aloha-type random-access protocols have been employed as access-control protocols in wireline and Wireless, and stationary and mobile, multiple-access communications networks. They are frequently employed by the control and signaling subsystem of demand-assigned multiple-Access protocols for regulating the sharing of a multiaccess communications channel. The correct design and sizing of the random-access operated control/signaling channel is a critical element in determining the performance of these networks. Excessive delays in the transport of signaling messages (induced by too many collisions and retransmissions) lead to unacceptable session-connection setup times. This is of particular concern when the message traffic is highly bursty, as it tends to be under a multitude of often-observed traffic-loading scenarios. Consequently, in this paper, we investigate the performance behavior of a random-access protocol when loaded by bursty traffic processes. The latter often exhibit long-range dependence (LRD). The LRD traffic flows are modeled here as multiplicative multifractal processes. The random-access protocol is modeled as an Aloha channel with blocking. We demonstrate that the burstiness feature of the traffic processes, rather than their LRD character, is the essential element determining the performance behavior of the protocol. When the loading-traffic process is not very bursty, we show that the performance of the random-access channel can be even better than that exhibited under Poisson traffic loading; otherwise, performance degradation is noted. We demonstrate the impact of the selection of the protocol-operational parameters in determining the effective performance behavior of the random-access protocol.