Title: Steady-state analysis of a slotted and controlled Aloha system with blocking
Abstract: We assume the reader is somewhat familiar with the ongoing development of Aloha techniques as described briefly in Abramson's FJCC 7 0 paper and Roberts's SJCC72 paper. In short, an Aloha system permits the (hopefully) occasional interference of data packet transmissions in a multi-access channel and provides for the retransmission of lost packets after some randomly distributed interval. The purposes behind permitting interference and providing recovery are (1) reduced central communication control to improve reliability and (2) improved use of communication facilites under bursty loads as found in interactive computer communication. Aloha techniques are finding applicability in various communication contexts (e.g., satellites), but here the emphasis is on large populations of (potentially mobile) interactive terminals. Slotted . In a slotted Aloha system, all terminals begin their packet (re)transmissions at the ' tick of some global clock. Slotting has been advocated by Roberts as a simple way to improve the limiting thruput of an Aloha channel by a factor of 2. Global ticking can be implemented in a (hopefully positive) number of ways and its feasibility is assumed in this paper. We rely on slotting to simplify our analysis, but suggest that the stability and control phenomena studied are characteristic of Aloha systems in general. Controlled . The notion of an optimal retransmission delay was introduced by Roberts. We extend the notion to include dynamic control of retransmission delay. A controlled Aloha system has the property that its terminals adjust their retransmission behavior as a function of perceived channel utilization. It will be shown that such adjustments are implementable in at least one way and that they improve system performance under heavy loads. Blocking and Thinking . When a user's terminal has a ready packet, it is assumed that no new packets can be generated. The user is said to be blocked . When a user is not blocked, he is said to be thinking . This assumption about user behavior departs from Abramson 's analysis and is thought to produce more realistic solutions. Recall that Abramson (in FJCC70) modelled users as unperturbable, realtime, Poisson sources of new packets. By adding blocking to an Aloha model, transmission delays feed back (as in real life) on the generation of transmission requests. User sessions are said to be dilated by transmissions delays. It is intended that think time account for (1) delays in central system response, (2) return transmission delays, (3) real user thinking time, and (4) type-in time. Block time accounts only for delays due to transmissions through the multi-access channel. The following analysis rests on some (very) simplifying assumptions about an Aloha system in equilibrium, in steady state. While having a large population of users tends to support our steady-state arguments, the dynamics do indeed require more detailed investigation.