Modelling and Simulation of Asynchronous Real-Time Systems using Timed Rebeca

In this paper we propose an extension of the Rebeca language that can be used to model distributed and asynchronous systems with timing constraints. We provide the formal semantics of the language using Structural Operational Semantics, and show its expressiveness by means of examples. We developed a tool for automated translation from timed Rebeca to the Erlang language, which provides a first implementation of timed Rebeca. We can use the tool to set the parameters of timed Rebeca models, which represent the environment and component variables, and use McErlang to run multiple simulations for different settings. Timed Rebeca restricts the modeller to a pure asynchronous actor-based paradigm, where the structure of the model represents the service oriented architecture, while the computational model matches the network infrastructure. Simulation is shown to be an effective analysis support, specially where model checking faces almost immediate state explosion in an asynchronous setting.Comment: In Proceedings FOCLASA 2011, arXiv:1107.584

On Synchronous and Asynchronous Monitor Instrumentation for Actor-based systems

We study the impact of synchronous and asynchronous monitoring instrumentation on runtime overheads in the context of a runtime verification framework for actor-based systems. We show that, in such a context, asynchronous monitoring incurs substantially lower overhead costs. We also show how, for certain properties that require synchronous monitoring, a hybrid approach can be used that ensures timely violation detections for the important events while, at the same time, incurring lower overhead costs that are closer to those of an asynchronous instrumentation.Comment: In Proceedings FOCLASA 2014, arXiv:1502.0315

Holistic assessment of call centre performance

In modern call centres 60–70% of the operational costs come in the form of the human agents who take the calls. Ensuring that the call centre operates at lowest cost and maximum efficiency involves a trade‐off of the cost of agents against lost revenue and increased customer dissatisfaction due to lost calls. Modelling the performance characteristics of a call centre in terms of the agent queue alone misses key performance influencers, specifically the interaction between channel availability at the media gateway and the time a call is queued. A blocking probability at the media gateway, as low as 0.45%, has a significant impact on the degree of queuing observed and therefore the cost and performance of the call centre. Our analysis also shows how abandonment impacts queuing delay. However, the call centre manager has less control over this than the level of contention at the media gateway. Our commercial assessment provides an evaluation of the balance between abandonment and contention, and shows that the difference in cost between the best and worst strategy is £130K per annum, however this must be balanced against a possible additional £2.98 m exposure in lost calls if abandonment alone is used

Approximations for the Moments of Nonstationary and State Dependent Birth-Death Queues

In this paper we propose a new method for approximating the nonstationary moment dynamics of one dimensional Markovian birth-death processes. By expanding the transition probabilities of the Markov process in terms of Poisson-Charlier polynomials, we are able to estimate any moment of the Markov process even though the system of moment equations may not be closed. Using new weighted discrete Sobolev spaces, we derive explicit error bounds of the transition probabilities and new weak a priori estimates for approximating the moments of the Markov processs using a truncated form of the expansion. Using our error bounds and estimates, we are able to show that our approximations converge to the true stochastic process as we add more terms to the expansion and give explicit bounds on the truncation error. As a result, we are the first paper in the queueing literature to provide error bounds and estimates on the performance of a moment closure approximation. Lastly, we perform several numerical experiments for some important models in the queueing theory literature and show that our expansion techniques are accurate at estimating the moment dynamics of these Markov process with only a few terms of the expansion