A Single Channel On/off Model with Tcp-like Control

We model behavior of a TCP-like source transmitting over a single channel to a server that processes work at constant rate r. Transmission by the source follows an on/oo mechanism. When the overall load in the system is below a critical constant , transmission rates increase linearly but when the load exceeds , then transmission rates decrease geometrically fast. We study the system by means of an embedded Markov chain which gives the buuer content at the start of transmissions. Attention is paid to the time necessary to transmit a le of size L and both the tail behavior and expectation of the distribution of le transmission time are considered. 1. Introduction Recent experimental work has shown that traac carried in high-speed networks, for example, Local Area Networks (LAN) 34], Wide Area Networks (WAN) 22] and Variable-Bit-Rate Video (VAR Video) 4], has features like long-range dependence and self-similarity which are strikingly diierent from those of traditional voice traac. Such observations have helped stimulate interest in the modeling and statistical analysis of traac in modern data networks. Modern data networks are robust and scalable and force congestion to stay with the end user. One of the networking features responsible for these good properties is the protocol TCP ((16]). TCP is the abbreviation for Transport Control Protocol and is responsible for controlling the rate of packet transmission by a sender and verifying the correct delivery of data packets to a destination. TCP adds support to detect error or lost packets and to trigger retransmission until the data is correctly and completely received. TCP controls transmission rates and roughly speaking can be thought to allow transmission rates to linearly increase until packet loss is detected by a lack of an acknowledgment at which time the rate of successive transmissions is halved until an acknowledgment comes back. Our goal is to nd a modest setting in which the eeect of a TCP-like control can be mathematically studied. In particular, since TCP is a decentralized mechanism for controlling transmission rates, we are interested in seeing the eeect of the control on a user who transmits a le. One of the interesting conclusions of our study is that the speciic manner in which geometric decrease occurs does not aaect the asymptotic form of the distribution of the time to transmit a le. Natural models for high-speed network traac include uid queues fed by on/oo sources with …