Stability of two interfering processors with load balancing

We examine the stability of two interfering processors with service rates depending on the number of users present of each of the classes and subject to static or dynamic load balancing. Such models arise in several contexts, especially in wireless networks, or multiprocessing. In case of static load balancing, we extend existing stability results by deriving Lyapunov functions that are connected to the solutions of one dimensional Poisson equation. We then characterize the optimal static load balancing. The Lyapunov function found for the static load balancing is used to derive the exact stability condition of an interesting class of dynamic load balancing policies. We show that for certain properties of the state-dependent service rates, simple dynamic load balancing schemes improve the stability condition. Keywords: Stability, Dynamic load balancing, State-dependent service rates, Lyapunov functions

Performance analysis of redundancy and mobility in multi-server systems

In this thesis, we studied how both redundancy and mobility impact the performance of computer systems and cellular networks, respectively. The general notion of redundancy is that upon arrival each job dispatches copies into multiple servers. This allows exploiting the variability of the queue lengths and server capacities in the system. We consider redundancy models with both identical and i.i.d. copies. When copies are i.i.d., we show that with PS and ROS, redundancy does not reduce the stability region. When copies are identical, we characterize the stability condition for systems where either FCFS, PS, or ROS is implemented in the servers. We observe that this condition strongly depends on the scheduling policy implemented in the system. We then investigate how redundancy impacts the performance by comparing it to a non-redundant system. We observe that both the stability and performance improve considerably under redundancy as the heterogeneity of the server capacities increases. Furthermore, for both i.i.d. and identical copies, we characterize redundancy-aware scheduling policies that improve both the stability and performance. Finally, we identify several open problems that might be of interest to the community. User mobility in wireless networks addresses the fact that users in a cellular network switch from cell to cell when geographically moving in the system. We control the mobility speed of the users among the servers and analyze how mobility impacts the performance at a user level. We observe that the performance of the system under fixed mobility speed strongly depends on the inherent parameters of the system