Performance evaluation is one of the key issues in design, modeling and optimization of complex networks. During the past year, research on performance analysis, including modeling, analysis (theoretical and simulation) and optimization has been focusing on two important issues: packet delay analysis and stationary tail asymptotics characterization. Packet delay is one the most important performance metrics in SONs. We have analyzed the packet delay for the selective-repeat automatic repeat request (SR-ARQ) protocol configured in a pair of a transmitter and a receiver. The analysis allowed us to accurately compute the mean re-sequencing delay in a SR-ARQ reliable communication network. Our analysis showed that the mean value of the re-sequencing delay at the steady state is almost a linear function of the packet error rate. Efforts to characterize tail asymptotics properties in joint distributions of stationary performance measures of a complex system have been made, including applications to a generalized join the shortest queue system, priority queues and processor sharing models. Tail asymptotics properties provide understanding of the dynamics in a complex system and performance bounds. This type of property is extremely important if closed-form solutions are not available, which is often the case for complex systems. Our recent results provided not only general properties about the tail asymptotics, but also relatively simple tools for applying the theory.
Control and allocation of resources for performance in network continue to strongly attract the interest of investigators. Although substantial research has been done in existing networks such as ATM and Internet, evolving networks following different operational principles present challenging problems in the area of control and management of networking resources. Optical networks have introduced these problems in the form of routing and wavelength assignment under the assumption that full wavelength conversion should be avoided as much as possible because it is not economical or even feasible to implement. We have been investigating the problem of optimal wavelength assignment in optical systems with no or limited wavelength conversion. We used the theory of Markov decision processes and dynamic programming to determine optimal wavelength allocation policies based on minimization of appropriate cost functions. The determination of such policies however, cannot be implemented in real time due to computational requirements. We extended our research and proposed heuristic policies that were compared through simulations with the optimal ones. We observed that the performance of the optimal and heuristic wavelength allocation policies was close enough therefore we concluded that the heuristic policies may be good candidates for implementation in practical problems. Similar ideas from stochastic control and Markov decision processes have been recently extended in research applied to wireless networks employing High-Speed Downlink Packet Access (HSDPA). In this problem we determined the optimal code allocation that has to be used by an HSDPA scheduler to transmit packets. The difference with the problems studied in the area of optical networks is that the medium in wireless networks is unreliable due to interference and fading. We first determined the optimal policies for codes allocation in the scheduler and then compared against heuristic/simpler to implement policies that can be used in practical systems.