Systems with queues
In Chapter 11 you learned about two approaches to simulating flows in systems. Both of them involved assuming the memory-less property. Also, neither of them simulated random variation in the modelled flow rates – that is, short-term, unpredictable fluctuations that often overlay more predictable patterns of behaviour. In this chapter you will learn about another approach, microsimulation, that is not constrained in these ways and you will use it to investigate some 'what-if questions about the number of beds in an intensive therapy unit.
This is also an opportunity to consider queues and the role of decision support systems in their management. Before going on to microsimulation techniques, you will learn how some simple queuing problems can be solved mathematically and how queuing theory can be used to make rapid estimates of mean queue length and service occupancy.
By the end of this chapter, you will be better able to:
• recognize queuing systems and describe their key features • define queue configuration and queue discipline • give theoretical results for simple queues • explain the mechanics of Monte Carlo simulation
Balking A queuing theory term for a situation where customers are 'lost' if all servers are
occupied when they arrive.
Customers Anyone or anything that requires a service or processing. Examples are outpatients
receiving treatment, or blood samples to be tested.
Deterministic models Models in which it is assumed that the nature of the relationships
between variables is known with certainty so that ('chaotic' systems excepted) for a given set of
starting values, the results are always the same.
Microsimulation A method of simulation based on modelling the experience of streams of
individual entities. Each entity can have its own set of attributes, and these may be altered
during the progress of the simulation. Thus a record can be kept of an entitity's 'history', and
the Markov assumption is unnecessary. It is usually combined with the Monte Carlo method
for sampling individuals' attributes and times to events.