Heavy traffic analysis of roving server networks

This paper studies the heavy-traffic (HT) behaviour of queueing networks with a single roving server. External customers arrive at the queues according to independent renewal processes and after completing service, a customer either leaves the system or is routed to another queue. This type of customer routing in queueing networks arises very naturally in many application areas (in production systems, computer- and communication networks, maintenance, etc.). In these networks, the single most important characteristic of the system performance is oftentimes the path time, i.e. the total time spent in the system by an arbitrary customer traversing a specific path. The current paper presents the first HT asymptotic for the path-time distribution in queueing networks with a roving server under general renewal arrivals. In particular, we provide a strong conjecture for the system's behaviour under HT extending the conjecture of Coffman et al. [E.G. Coffman Jr., A.A. Puhalskii, M.I. Reiman 1995 and 1998] to the roving server setting of the current paper. By combining this result with novel light-traffic asymptotics we derive an approximation of the mean path-time for arbitrary values of the load and renewal arrivals. This approximation is not only highly accurate for a wide range of parameter settings, but is also exact in various limiting cases

Optimal Control of Parallel Queues for Managing Volunteer Convergence

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/163497/2/poms13224.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/163497/1/poms13224_am.pd

Optimal and Heuristic Resource Allocation Policies in Serial Production Systems

We have studied the optimal server allocation policies for a tandem queueing system under different system settings. Motivated by an industry project, we have studied a two stage tandem queueing system with arrival to the system and having two flexible servers capable of working at either of the stations. In our research, we studied the system under two different circumstances: modeling the system to maximize throughput without cost considerations, modeling the system to include switching and holding costs along with revenue for finished goods. In the maximizing throughput scenario, we considered two different types of server allocations: collaborative and non-collaborative. For the collaborative case, we identified the optimal server allocation policies for the servers and have proved the structure of the optimal server allocation policy using mathematical iteration techniques. Moreover, we found that, it is optimal to allocate both the servers together all the time to get maximum throughput. In the non-collaborative case, we have identified the optimal server allocation policies and found that it is not always optimal to allocate both the servers together. With the inclusion of costs, we studied the system under two different scenarios: system with switching costs only and system having both switching and holding costs. In both the cases, we have studied the optimal server allocation policies for the servers. Due to the complicated structure of the optimal server allocation policy, we have studied three different heuristics to approximate the results of the optimal policy. We found that the performance of one of the heuristics is very close to the optimal policy values

Optimal control of a deterministic multiclass queuing system by serving several queues simultaneously

In this report we consider the optimal control problem of emptying a deterministic single server multiclass queuing system without arrivals. We assume that the server is able to serve several queues simultaneously, each at its own rate, independent of the number of queues being served. We showed that the optimal sequence of modes is ordered by rate of cost decrease. However, queues are not necessarily emptied. We propose a dynamic programming approach for solving the problem, which reduces the multiparametric QP (mpQP) to a series of problems that can be solved readily

Iterative approximation of k-limited polling systems

The present paper deals with the problem of calculating queue length distributions in a polling model with (exhaustive) k-limited service under the assumption of general arrival, service and setup distributions. The interest for this model is fueled by an application in the field of logistics. Knowledge of the queue length distributions is needed to operate the system properly. The multi-queue polling system is decomposed into single-queue vacation systems with k-limited service and state-dependent vacations, for which the vacation distributions are computed in an iterative approximate manner. These vacation models are analyzed via matrix-analytic techniques. The accuracy of the approximation scheme is verified by means of an extensive simulation study. The developed approximation turns out be accurate, robust and computationally efficient