Steady-state analysis of a slotted and controlled Aloha system with blocking

• Authors: Bob Metcalfe
• Venue: ACM SIGCOMM Computer Communication Review
• Year: 1975

We assume the reader is somewhat familiar with the ongoingdevelopment of Aloha techniques as described briefly in Abramson'sFJCC 7 0 paper and Roberts's SJCC72 paper. In short, an Alohasystem permits the (hopefully) occasional interference of datapacket transmissions in a multi-access channel and provides for theretransmission of lost packets after some randomly distributedinterval. The purposes behind permitting interference and providingrecovery are (1) reduced central communication control to improvereliability and (2) improved use of communication facilites underbursty loads as found in interactive computer communication. Alohatechniques are finding applicability in various communicationcontexts (e.g., satellites), but here the emphasis is onlarge populations of (potentially mobile) interactiveterminals.Slotted. In a slotted Aloha system, all terminalsbegin their packet (re)transmissions at the ' tick of some globalclock. Slotting has been advocated by Roberts as a simple way toimprove the limiting thruput of an Aloha channel by a factor of 2.Global ticking can be implemented in a (hopefully positive) numberof ways and its feasibility is assumed in this paper. We rely onslotting to simplify our analysis, but suggest that the stabilityand control phenomena studied are characteristic of Aloha systemsin general.Controlled. The notion of an optimal retransmission delaywas introduced by Roberts. We extend the notion to include dynamiccontrol of retransmission delay. A controlled Aloha systemhas the property that its terminals adjust their retransmissionbehavior as a function of perceived channel utilization. It will beshown that such adjustments are implementable in at least one wayand that they improve system performance under heavy loads.Blocking and Thinking. When a user's terminal has a readypacket, it is assumed that no new packets can be generated. Theuser is said to be blocked. When a user is not blocked, heis said to be thinking. This assumption about user behaviordeparts from Abramson 's analysis and is thought to produce morerealistic solutions. Recall that Abramson (in FJCC70) modelledusers 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. Usersessions are said to be dilated by transmissions delays.It is intended that think time account for (1) delays incentral system response, (2) return transmission delays, (3) realuser thinking time, and (4) type-in time. Block timeaccounts only for delays due to transmissions through themulti-access channel.The following analysis rests on some (very) simplifyingassumptions about an Aloha system in equilibrium, in steady state.While having a large population of users tends to support oursteady-state arguments, the dynamics do indeed require moredetailed investigation.