We introduce the process number of a digraph as a tool to study rerouting issues in wdm networks. This parameter is closely related to the vertex separation (or pathwidth). We consider the recognition and the characterization of (di)graphs with small process number. In particular, we give a linear time algorithm to recognize (and process) graphs with process number at most 2, along with a characterization in terms of forbidden minors, and a structural description. As for digraphs with process number 2, we exhibit a characterization that allows to recognize (and process) them in polynomial time. Key words: Rerouting, process number, vertex separation, pathwidth. 1

Abstract not found

Real-life telecommunications systems and computer networks are often modelled as stochastic service systems. This thesis contributes to the fields of performance analysis and/or resource optimization for two representative stochastic service sys-tems: 1) a finite buffer time-division multiple-access (TDMA) system, and 2) a large scale video-on-demand (VOD) service system. For the first problem, we provide delay analysis for a class of finite buffer TDMA systems. We first extend the traditional finite buffer TDMA model with constant ser-vice rate to one that considers a state-dependent stochastic service process. The con-siderable versatility associated with this service process allows the resulting TDMA model to generalize all constant service models that have been so far investigated in the literature. More importantly, it enables the new model to cater for a wider range of applications such as the analysis of paging performance in GSM networks [81] and the modelling of edge routers in time-slotted optical burst switching (OBS) networks [163]. For this new model, we present a detailed analysis for the den-sity and cumulative distribution of the waiting time experienced by an arbitrary

Abstract—In this paper, we propose a bandwidth-efficient multicast mechanism for heterogeneous wireless networks. We reduce the bandwidth cost of an Internet Protocol (IP) multicast tree by adaptively selecting the cell and the wireless technology for each mobile host to join the multicast group. Our mechanism enables more mobile hosts to cluster together and leads to the use of fewer cells to save the scarce wireless bandwidth. Besides, the paths in the multicast tree connecting to the selected cells share more common links to save the wireline bandwidth. Our mechanism supports the dynamic group membership and offers mobility of group members. Moreover, our mechanism requires no modification to the current IP multicast routing protocols. We formulate the selection of the cell and the wireless technology for each mobile host in the heterogeneous wireless networks as an optimization problem. We use Integer Linear Programming to model the problem and show that the problem is NP-hard. To solve the problem, we propose a distributed algorithm based on Lagrangean relaxation and a network protocol based on the algorithm. The simulation results show that our mechanism can effectively save the wireless and wireline bandwidth as compared to the traditional IP multicast. Index Terms—Heterogeneous wireless networks, multicast. Ç 1