Analysis and decentralised optimal flow control of heterogeneous computer communication network models - Ku-Mahamud, Ku Ruhana (1993)
General closed queueing networks are used to model the local flow control in multiclass computer communication networks with single and multiple transmission links. The problem of analysing multiclass general closed queueing network models with single server and multiserver is presented followed by the problem of the centralised optimal local flow control of multiclass general computer communication networks with single and multiple transmission links. The generalised exponential (GE) distributional model with known first two moments has been used to represent general interarrival and transmission time distributions as various users have various traffic characteristics. A new method of general model reduction using the Norton' s theorem for general queueing networks in conjunction with the universal maximum entropy algorithm is proposed for the analysis of xix large general closed queueing networks. This extension to Norton 's theorem has an advantage over the direct application of the universal maximum entropy approach whereby the study of a subset of queueing centres of interest can be done without repeatedly solving the entire network. The principle of maximum entropy is used to derive new approximate solutions for the joint queue length distributions of multiclass general queueing network models with single server and multiserver and favourable comparisons with other methods are made. The decentralised optimal local flow control of the multiclass computer communication networks with single and multiple transmission links is shown to be a state dependent window type mechanism that has been traditionally used in practice. The maximum number of packets in transit within the system corresponding to a maximum throughput and can be determined from a preassigned upper bound on the mean time delay, the average allowed load and the parameters of the underlying systems. The direct dependence of the maximum throughput on the mean time delay is also determined. The optimal local flow control with global objectives results in a team decision that does not favour any individual user, and depends only on the relative order of their packet generation rates. Numerical examples provide useful informations on how critically system behaviour is affected by (i) the distributional form of the interarrival and transmission patterns, (ii) the maximum input rate. The analytic results described in this thesis suggest that (i) analytical analysis for general closed queueing networks which are used to model computer communication networks can be analysed using the principle of maximum entropy, (ii) congestion problems in computer communication networks with non-exponential data flows should be examined in terms of maximum throughput under a time delay constraint where the offered load appears only as a parameter.