On pseudo-conservation laws for the cyclic server system with compound Poisson arrivals

Boxma and Groenendijk obtain the pseudo-conservation laws for cyclic server systems, for both the continuous-time system with simple Poisson arrivals, and for the discrete-time system. We extend these laws to the continuous-time cyclic server system with compound Poisson arrivals. In the process we identify an error in Boxma and Groenendijk's analysis of the semi-exhaustive service strategy in the discrete-time cyclic server system.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29064/1/0000097.pd

Mixed Polling with Rerouting and Applications

Queueing systems with a single server in which customers wait to be served at a finite number of distinct locations (buffers/queues) are called discrete polling systems. Polling systems in which arrivals of users occur anywhere in a continuum are called continuous polling systems. Often one encounters a combination of the two systems: the users can either arrive in a continuum or wait in a finite set (i.e. wait at a finite number of queues). We call these systems mixed polling systems. Also, in some applications, customers are rerouted to a new location (for another service) after their service is completed. In this work, we study mixed polling systems with rerouting. We obtain their steady state performance by discretization using the known pseudo conservation laws of discrete polling systems. Their stationary expected workload is obtained as a limit of the stationary expected workload of a discrete system. The main tools for our analysis are: a) the fixed point analysis of infinite dimensional operators and; b) the convergence of Riemann sums to an integral. We analyze two applications using our results on mixed polling systems and discuss the optimal system design. We consider a local area network, in which a moving ferry facilitates communication (data transfer) using a wireless link. We also consider a distributed waste collection system and derive the optimal collection point. In both examples, the service requests can arrive anywhere in a subset of the two dimensional plane. Namely, some users arrive in a continuous set while others wait for their service in a finite set. The only polling systems that can model these applications are mixed systems with rerouting as introduced in this manuscript.Comment: to appear in Performance Evaluatio

Optimization of polling systems with Bernoulli schedules

Optimization;Polling Systems;Queueing Theory;operations research

Analysis of a queuing model for slotted ring networks

We study a multi-server multi-queue system which is intended to model a local area network with slotted ring protocol. Two special cases of the model are analysed and the results are used to motivate an approach to approximate mean queue lengths in the general model

Waiting times in discrete-time cyclic-service systems

Single-served, multiqueue systems with cyclic service in discrete time are considered. Nonzero switchover times between consecutive queues are assumed; the service strategies at the various queues may differ. A decomposition for the amount of work in such systems is obtained, leading to an exact expression for a weighted sum of the mean waiting times at the various queues

Non-Abelian current oscillations in harmonic string loops: existence of throbbing vortons

It is shown that a string carrying a field of harmonic type can have circular vorton states of a new "throbbing" kind, for which the worldsheet geometry is stationary but the internal structure undergoes periodic oscillation.Comment: 14 pages Latex, colored version of manuscript originally published in black and whit