The increase of the instability of networks due to Quasi-Static link capacities

Authors:
Dimitrios Koukopoulos;Marios Mavronicolas;Paul Spirakis
Affiliations:
Department of Applied Informatics in Management and Finance, Technological Education Institute of Ionian Islands, Greece and RACTI, 61 Riga Fereou, 26221 Patras, Greece;Department of Computer Science, University of Cyprus, 1678 Nicosia, Cyprus and Faculty of Computer Science, Electrical Engineering and Mathematics, University of Paderborn, 33102 Paderborn, German ...;Department of Computer Engineering and Informatics, University of Patras, Greece and RACTI, 61 Riga Fereou, 26221 Patras, Greece
Venue:
Theoretical Computer Science
Year:
2007

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Abstract

In this work, we study the impact of the dynamic changing of the network link capacities on the stability properties of packet-switched networks. Especially, we consider the Adversarial, Quasi-Static Queuing Theory model, where each link capacity may take on only two possible (integer) values, namely 1 and C1 under a (w,@r)-adversary. We obtain the following results: *Allowing such dynamic changes to the link capacities of a network with just ten nodes that uses the LIS (Longest-in-System) protocol for contention-resolution results in instability at rates @r2-1 and for large enough values of C. *The combination of dynamically changing link capacities with compositions of contention-resolution protocols on network queues suffices for similar instability bounds: The composition of LIS with any of SIS (Shortest-in-System), NTS (Nearest-to-Source), and FTG (Furthest-to-Go) protocols is unstable at rates @r2-1 for large enough values of C. *The instability bound of the network subgraphs that are forbidden for stability is affected by the dynamic changes to the link capacities: we present improved instability bounds for all the directed subgraphs that were known to be forbidden for stability on networks running a certain greedy protocol.