Motivated by assembly processes, we consider a Markovian queueing system with multiple coupled queues and customer impatience. Coupling means that departures from all constituent queues are synchronised and that service is interrupted whenever any of the queues is empty and only resumes when all queues are non-empty again. Even under Markovian assumptions, the state-space grows exponentially with the number of queues involved. To cope with this inherent state-space explosion problem, we investigate performance by means of two numerical approximation techniques based on series expansions, as well as by deriving the fluid limit. In addition, we provide closed-form expressions for the first terms in the series expansion of the mean queue content for the symmetric coupled queueing system. By an extensive set of numerical experiments, we show that the approximation methods complement each other, each one being accurate in a particular subset of the parameter space.

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This paper investigates the performance of a queueing model with multiple finite queues and a single server. Departures from the queues are synchronised or coupled which means that a service completion leads to a departure in every queue and that service is temporarily interrupted whenever any of the queues is empty. We focus on the numerical analysis of this queueing model in a Markovian setting: the arrivals in the different queues constitute Poisson processes and the service times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we calculate the terms in the series expansion in the service rate of the stationary distribution of the Markov chain as well as various performance measures when the system is (i) overloaded and (ii) under intermediate load. Our numerical results reveal that, by calculating the series expansions of performance measures around a few service rates, we get accurate estimates of various performance measures once the load is above 40% to 50%.

This paper introduces a performance analysis tool for a wireless access point serving multiple mobile nodes. The channel conditions vary over time and the opportunistic scheduler in the access point can account for the channel conditions as well as for the number of backlogged packets for the different mobile nodes. The tool allows for fast and accurate calculations of the main performance measures of the system. Calculations are based on a Maclaurin series expansion of the solution of the Markov process that describes the channel conditions and the queue contents for the different mobile nodes. The Maclaurin series expansion only requires the inversion of sparse block triangular matrices, which is considerably faster than directly calculating the solution. The tool provides a user interface for defining the network and channel parameters and can be used for assessing the efficiency of opportunistic schedulers, or for optimizing system parameters and scheduling policies of such schedulers.