Bounded Mean-Delay Throughput and Non-Starvation Conditions in Aloha   Network
  This paper considers the requirements to ensure bounded mean queuing delay and non-starvation in a slotted Aloha network operating the exponential backoff protocol. It is well-known that the maximum possible throughput of a slotted Aloha system with a large number of nodes is 1/e = 0.3679. Indeed, a saturation throughput of 1/e can be achieved with an exponential backoff factor of r = e/(e-1)=1.5820. The binary backoff factor of r = 2 is assumed in the majority of prior work, and in many practical multiple-access networks such as the Ethernet and WiFi. For slotted Aloha, the saturation throughput 0.3466 for r = 2 is reasonably close to the maximum of 1/e, and one could hardly raise objection to adopting r = 2 in the system. However, this paper shows that if mean queuing delay is to be bounded, then the sustainable throughput when r = 2 is only 0.2158, a drastic 41% drop from 1/e . Fortunately, the optimal setting of r = 1.3757 under the bounded mean-delay requirement allows us to achieve sustainable throughput of 0.3545, a penalty of only less than 4% relative to 1/e. A general conclusion is that the value of r may significantly affect the queuing delay performance. Besides analyzing mean queuing delay, this paper also delves into the phenomenon of starvation, wherein some nodes are deprived of service for an extended period of time while other nodes hog the system. Specifically, we propose a quantitative definition for starvation and show that the conditions to guarantee bounded mean delay and non-starved operation are one of the same, thus uniting these two notions. Finally, we show that when mean delay is large and starvation occurs, the performance results obtained from simulation experiments may not converge. A quantitative discussion of this issue is provided in this paper. 
Soung Chang Liew, Ying Jun Zhang, Da Rui Chen