Network Protocol Performance Bounding Exploiting Properties of Infinite Dimensional Linear Equations ⋆

Abstract. This paper presents a quite versatile and widely applicable performance analysis methodology that has been applied for the study of network resource allocation protocols in the past. It is based on the identification ofrenewal cycles of theoperation of thesystem andthe setting up of recursive equations with respect to quantities-indices defined over the renewal cycles and sessions that appear within. Application of the expectation operator on these equations leads to infinite dimensional systems of linear equations which are shown to posses certain properties leading to rigorous and almost arbitrarily tight bounds on various performance metrics of interest. The special case of a random access protocol is used as an example in order to illustrate the derivation of the recursive equations capturing the protocol dynamics and system inputs. Finally, some other examples of application of the methodology are briefly discussed, illustrating the versatility and powerfulness of the approach. This analysis methodology can be quite useful for understanding the behavior of current complex and large scale networking environments, as well as assessing their scalability, stability and performance.

Leader election in ad hoc radio networks: A keen ear helps

We address the fundamental distributed problem of leader election in ad hoc radio networks modeled as undirected graphs. Nodes are stations having distinct integer labels, and each node knows only its own label and a polynomial upper bound on all labels. A signal from a transmitting node reaches all neighbors. What distinguishes radio networks from message-passing networks is that a message is received successfully by a node, if and only if, exactly one of its neighbors transmits in this round. If two neighbors of a node transmit simultaneously in a given round, none of the messages is heard by the receiving node. In this case we say that a collision occurred at this node. An important capability of nodes of a radio network is collision detection:the ability of nodes to distinguish a collision from the background noise occurring when no neighbor transmits. (This ability is the “keen ear ” of the nodes.) Can collision detection speed up leader election in arbitrary radio networks? We give a positive answer to this question. More precisely, our main result is a deterministic leader election algorithm working in time O(n) in all n-node networks, if collision detection is available, while it is known that deterministic leader election requires time Ω(nlog n), even for complete networks, if there is no collision detection. This is the first computational task whose execution for arbitrary radio networks is shown to be faster with collision detection than without it