1 Department of Informatics and Mathematical Modeling, Technical University of Denmark
The dissertation is concerned with modelling various performance aspects pertaining to packet switched telecommunication networks. The emphsis has been put on versatile modelling of the packet arrival process which is a very relevant issue in cotext with the future Broadband Integrated Service Data Network (B-ISDN). As a case study of packet switched networks Common Channel Signalling System No. 7(SS7) has been used. SS7 is the packet switched network currently employed to command/control the public switched telephone network i.e. the setup and teardown of trunks and the basis for intelligent network services i.e. 800 and 900 calls and advanced mobile communication services. The Markovian Arrival Process (MAP) has been used as a versatile tool to model the packet arrival process. Applying the MAP facilitates the use of Matrix Analytic methods to obtain performance measures associated with for example the single server queue with a MAP arrival process and a general service time distribution. Measured SS7 traffic data has been analyzed as a part of this study. Recently there has been expressed concern regarding adverse behaviour of measured SS7 traffic i.e. long range dependence. Our studies did vot reveal any adverse behaviour. In fact the observed traffic seemed very close to what would be expected from Poisson traffic. The Changeover/Changeback procedure in SS7, which is used to redirect traffic in case of link failure, has been analyzed. The transient behaviour during a Changeover scenario was modelled using Markovian models. The Ordinary Differential Equations arising from these models were solved numerically. The results obtained seemed very similar to those obtained using a different method in previous work by Akinpelu & Skoog 1985. Recent measurement studies of packet traffic from Local Area Networks (LAN) carried out at Bell Communications Research (Bellcore), New Jersey, have revealed behaviour very different from what conventional teletraffic models assume. In fact the observed traffic displays behaviour with (second order) self-similar characteristics over several time-scales. In this study we show that 8-16 state MAPs are able to capture this very variable behaviour over several timescales. The queueing behaviour of these MAPs has been analyzed with Matrix Analytic methods. The results correspond to those obtained by trace driven simulations of measured LAN traffic. It is shown that two arrival processes with the same first and second order properties of their counting processes can yield substantially different queueing behaviour. This illustrates that one should by very careful when trying to assess queueing behaviour from the first and second order properties of the arrival process. A heuristic formula for the tail behaviour of a single server queue fed by a superposition of renewal processes has been evaluated. The evaluation was performed by applying Matrix Analytic methods. The heuristic formula has applications in the Call Admission Control (CAC) procedure of the future BISDN network. The heuristic formula did not seem to yield substantially better results than already available approximations. Finally, some results for the finite capacity BMAP/G/1 queue have been obtained. The steady state probability vector of the embedded chain is found by a direct method where a modified LU factorisation scheme is employed. The standard LU factorisation scheme is modified so that all computations are done concellation free and in a manner that exploits the special structure of the embedded chain yielding substantial computational savings. The queue- length at an arbitrary time is found by noting the close relationship with the expressions for the corresponding infinite queue. For the special case of a batch Poisson arrival process this observation makes it possible to express the queue length at an arbitrary in terms of the corresponding queue lengths for the infinite case.