Packet Forwarding Algorithms in a Line Network

Abstract. We initiate a competitive analysis of packet forwarding poli-cies for maximum and average flow in a line network. We show that the policies Earliest Arrival and Furthest-To-Go are scalable, but not con-stant competitive, for maximum flow. We show that there is no constant competitive algorithm for average flow.

Scheduling in Networks with Limited Buffers

In networks with limited buffer capacity, packet loss can occur at a link even when the average packet arrival rate is low compared to the link's speed. To offer strong loss-rateguarantees, ISPs may need to adopt stringent routing constraints to limit the load at the network links and the routing path length. However, to simultaneously maximize revenue, ISPs should be interested in scheduling algorithms that lead to the least stringent routing constraints. This work attempts to address the ISPs needs as follows. First, by proposing an algorithm that performs well (in terms of routing constraints) on networks of output queued (OQ) routers (that is, ideal routers), and second, by bounding the extra switch fabric speed and buffer capacity required for the emulationof these algorithms in combined input-output queued (CIOQ) routers.The first part of the thesis studies the problem of minimizing the maximum session loss rate in networks of OQ routers. It introduces the Rolling Priority algorithm, a local online scheduling algorithm that offers superior loss guarantees compared to FCFS/Drop Tail and FCFS/Random Drop. Rolling Priority has the following properties: (1) it does not favor any sessions over others at any link, (2) it ensures a proportion of packets from each session are subject to a negligibly small loss probability at every link along the session's path, and (3) maximizes the proportion of packets subject to negligible loss probability. The second part of the thesis studies the emulation of OQ routers using CIOQ. The OQ routers are equipped with a buffer of capacity B packets at every output. For the family of work-conserving scheduling algorithms, we find that whereas every greedy CIOQ policy is valid for the emulation of every OQ algorithm at speedup B, no CIOQ policy is valid at speedup less than the cubic root of B-2 when preemption is allowed. We also find that CCF, a well-studied CIOQ policy, is not valid at any speedup less than B. We then introduce a CIOQ policy CEH, that is valid at speedup greater than the square root of 2(B-1)

Information gathering in ad-hoc radio networks with tree topology

We study the problem of information gathering in ad-hoc radio networks, focusing on the case when the network forms a tree, with edges directed towards the root. Initially, each node has a rumor, and we aim to deliver all rumors to the root as quickly as possible without knowing the tree's topology in advance. In the deterministic case, where nodes are labeled with small integers, we give an -time protocol for the model with unbounded message size, and an -time protocol for bounded message size. We also consider fire-and-forward protocols, in which nodes can transmit only their own rumor or the rumor received in the previous step. We give a deterministic fire-and-forward protocol with running time , and show that it is asymptotically optimal. We also present a randomized -time protocol in the model without node labels or aggregation, and show that it is asymptotically optimal

Packet Routing and Information Gathering in Lines, Rings and Trees

Abstract We study the problem of online packet routing and information gathering in lines, rings andtrees. A network consists of n nodes. At each node there is a buffer of size B. Each buffer cantransmit one packet to the next buffer at each time step. The packets injection is under adversarial control. Packets arriving at a full buffer must be discarded. In information gathering all packetshave the same destination. If a packet reaches the destination it is absorbed. The goal is to maximize the number of absorbed packets. Previous studies have shown that even on the linetopology this problem is difficult to handle by online algorithms. A lower bound of \Omega (p n) onthe competitiveness of the Greedy algorithm was presented by Aiello et al in [2]. All other known algorithms have a polynomial competitive ratio. In this paper we give the first O(log n) competitivedeterministic algorithm for the information gathering problem in lines, rings and trees. We also consider multi-destination routing where the destination of a packet may be any node. For lines andrings we show an O(log2 n) competitive randomized algorithms. Both for information gatheringand for the multi-destination routing our results improve exponentially the previous results. 1 Introduction Overview: Packet routing networks, have become dominant platform for carrying data. In this paperwe investigate a packet routing and information gathering in lines, rings and trees. In information gathering all injected packets have the same destination. Information gathering is widely used inmany networks (e.g sensor networks). We also consider the multi destination routing in which the destination of a packet might be any node in the network. We model the problem of packet routing on a unidirectional line or ring or tree as follows. Anetwork ha