Comparing the performance measures of the M/M/1 and the G/G/1 queueing models through an agent based simulation

Details

Supervisors

Chevalier, Philippe

Faculty

Louvain School of Management

Degree label

Master [120] en Ingénieur de gestion

Abstract

How long does it take you to go to work every day? How long before your internet page is loaded? How many people will there be in line in front of you at the check-out counter? When we think about it, we realise just how much variability is present around us and how much we can’t face it. However, it wasn’t until my years at university, my first year on the job and my first readings for this paper that I realised just how much it is important to be able to measure that variability and to track its performance. The performance tracking is a phenomenon that has always been present but that has increased in importance in the last decades or years. The sales representative that now has to write down his meetings in a system to analyse hit performances; the footballer that not only gets rated on the success of his team but needs to perform individually and show the best statistics at the end of the day etc. Those are examples of situations where performance analysis is crucial for further development. Of course, performance analysis can be calculated for certain and precise situations but what is the point if we have to do this for every single situation. What we want is to have a model that could be applied to many situations to show us their overall performance and this is what queueing theory, and this paper, will focus on. The first chapter will focus on the analysis of a simple queueing model following easy assumptions and giving quick results while the second chapter will focus on a larger model that will require more calculations but might give some more accurate results. In each case the modelled system will be a single server with a single queue. Each chapter will start off with a theoretical part resuming existing literature specific to that model. The second part of each chapter will aim to confirm those results by simulating the system in AnyLogic, a multimethod simulation modelling tool. The goal of this paper was to identify and evaluate performance measure indicators that could be applied to real life situations and could guide people in managing such a system. In the first chapter we focused on the analysis of a simple queueing model. We used the simple M/M/1 model to represent a system with a single server and an infinite queue. We were able to obtain formulas for the different performance measures, our cycle time and work in progress for both our system as a whole and the queue. This analysis highlighted the ease of use of the M/M/1 model but also identified some gaps with the reality due to the assumptions that were necessary and that do not necessarily fit with real life situations. Nonetheless, the M/M/1 is a good approximation of our model if we do not have much information about it. We should just be aware of the fact that the chances of errors are bigger as we might not account our system for its real variability. In the second chapter we worked with a G/G/1 model that, due to its generalised distribution was more fitted to the reality of most single server systems. Unfortunately, this increase in realism requires more information in terms of input and some good system analysis is necessary beforehand to be able use the identified formulas. In addition, even if this model includes more elements from the reality the G/G/1 also highlights the fact that we can’t find a single formula defining our performance but rather an interval in which we can be sure to be located. In both chapters we were able to start off with some theoretical background that would give us a better overview on the trends that could exist as well as their impacts. More than the absolute values it is the relative changes that should grab the reader’s attention. When analysing its own system it can be highly interesting to do a scenario analysis and observe how The goal of this paper was achieved as the reader could understand the behaviours and trends going on in a system as well as they expected performance of that system but this leaves the question of the actual improvement process open. This is not part of the scope of this project but might be a subject for further analysis to provide the reader with an actual action plan regarding its server.