Using a controlled Jackson network as the primary example, stochastic control problems are formulated as martingale problems and the optimal solutions are characterized as the solutions of infinite dimensional linear programs. Assuming a heavy traffic scaling, the analogous linear program for a singular control problem is derived, and the solution of the linear program is shown to give the stoc...

In this paper, we propose a sampler for the product-form solution of basic queueing networks, closed Jackson networks with single servers. Our approach is sampling via Markov chain, but it is NOT a simulation of behavior of customers in queueing networks. We propose a new ergodic Markov chain whose unique stationary distribution is the product form solution of a closed Jackson Network, thus we ...

What explains the large variation in the number of contacts (degree) that different participants of social networks have: age, randomness, or some unobservable fitness measure? To answer this question, I extend the model presented in Jackson and Rogers (2007) to allow individuals to vary in their ability to attract contacts. I estimate the parameters of the extended model, using a social networ...

Balanced likelihood ratio importance sampling methods were originally developed for the analysis of fault-tolerant systems. This paper provides a basis for adapting this approach to analyze the rare event probability that total system size reaches a bound before returning to zero in tandem Jackson networks. An optimal importance sampling distribution for the single server case is derived throug...

Network situations as introduced by Jackson and Wolinsky (1996) incorporate the influence of the architecture of a network rather than just the connectivity it provides and thereby provide a more flexible setting than communication situations, which consist of a game with transferable utility and a network. We characterize the position value for network situations along the lines of the charact...

Traffic congestion is increasing in over populated urban areas, our traditional traffic management system can no longer solve this problem. However, problem be solved by converting road networks into queueing networks. This paper proposes, the use of an open Jackson Queueing Model which equated with existing network to calculate waiting time vehicles network, further processed put optimized sta...