This dissertation consists of two parts. The first part delves into the problem of response time estimation in fork-join queueing networks. These systems have been seen in literature for more than thirty years. The estimation of the mean response time in these systems has been found to be notoriously hard for most forms of these queueing systems. In this work, simple expressions for the mean response time are proposed as conjectures. Extensive experiments demonstrate the remarkable accuracy of these conjectures. Algorithms for the estimation of response time using these conjectures are proposed. For many of the networks studied in this dissertation, no approximations are known in literature for estimation of their response time. Therefore, the contribution of this dissertation in this direction marks significant progress in the analysis of fork-join queues. The second part of this dissertation introduces a fractional version of the classical maximum weight clique problem, the maximum ratio clique problem, which is to find a maximal clique that has the largest ratio of benefit and cost weights associated with the cliques vertices. This problem is formulated to model networks in which the vertices have a benefit as well as a cost associated with them. The maximum ratio clique problem finds applications in a wide range of areas including social networks, stock market graphs and wind farm location. NP-completeness of the decision version of the problem is established, and three solution methods are proposed. The results of numerical experiments with standard graph instances, as well as with real-life instances arising in finance and energy systems, are reported.
