Zero-automatic queues and product form

We introduce and study a new model: 0-automatic queues. Roughly, 0-automatic queues are characterized by a special buffering mechanism evolving like a random walk on some infinite group or monoid. The salient result is that all stable 0-automatic queues have a product form stationary distribution and a Poisson output process. When considering the two simplest and extremal cases of 0-automatic queues, we recover the simple M/M/1 queue, and Gelenbe's G-queue with positive and negative customers

Sojourn times in the M/G/1 FB queue with light-tailed service times

The asymptotic decay rate of the sojourn time of a customer in the stationary M/G/1 queue under the Foreground-Background (FB) service discipline is studied. The FB discipline gives service to those customers that have received the least service so far. We prove that for light-tailed service times the decay rate of the sojourn time is equal to the decay rate of the busy period. It is shown that FB minimises the decay rate in the class of work-conserving disciplines

Analysis and Computation of the Joint Queue Length Distribution in a FIFO Single-Server Queue with Multiple Batch Markovian Arrival Streams

This paper considers a work-conserving FIFO single-server queue with multiple batch Markovian arrival streams governed by a continuous-time finite-state Markov chain. A particular feature of this queue is that service time distributions of customers may be different for different arrival streams. After briefly discussing the actual waiting time distributions of customers from respective arrival streams, we derive a formula for the vector generating function of the time-average joint queue length distribution in terms of the virtual waiting time distribution. Further assuming the discrete phase-type batch size distributions, we develop a numerically feasible procedure to compute the joint queue length distribution. Some numerical examples are provided also

Priority allocation decisions in large scale MTO/MTS multi-product manufacturing systems : Technical report

In this paper, the authors consider a single stage multi-product manufacturing facility producing a large number of end-products for delivery within a service constraint for the customer lead-time. The manufacturing facility is modeled as a multi-product, multi-priority queuing system. In order to reduce inventory costs, an e±cient priority allocation between items consists in producing some items according to a Make-To-Stock (MTS) policy and others according to a Make-To-Order (MTO)policy epending on their features (costs, required lead-time, demand rates). The authors propose a general optimization procedure that gives a near-optimal °ow control (MTO or MTS) to associate with each product and the corresponding near-optimal priority strategy. We illustrate e±ciency of our procedure via several examples and by a numerical analysis. In addition, we show numerically that a small number of priority classes is su±cient to obtain near-optimal performances.Make-to-Stock (MTS); Make-to-Order (MTO); Priority allocation; Scheduling rule; Heterogeneous multi-product queuing system