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The Markov Chain Model

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Queuing models are an abstraction of Markov chain models. On assessing their empirical validity to assign patrols to City police stations, it has been concluded that queuing theory provides good approximations of the system behaviour. We configure a fleet whose vehicles get calls while on the route. The objective is to minimize operating costs subject to several constraints, including a maximum waiting time for customers, modelled using queuing formulas. Besides the Markov chain and the queuing models, an ambulance service can be studied by computer simulation. It is particularly suitable when the parameters are unknown or not homogeneous. Although simulation allows for detailed descriptions, its applicability is limited by its high implementation …show more content…

In Section 2 we have explained the assumptions we make regarding ambulance logistics, and introduce the decision variables and parameters. In Section 3 we show the key performance indicators (KPI) that concern the manager (3.1) and the patient (3.2). Section 4 presents the case of an ambulance firm. It evaluates its present performance as a function of the resources deployed (4.1), identifies the main opportunities for operational improvement (4.2), and optimizes the geographic coverage (4.3). Last section presents our main …show more content…

o The occurrence of an emergency to a person does not determine subsequent occurrences. This memory-less assumption is debatable: past emergencies might influence future ones. o Total demand is the sum of homogeneous and non-correlated people's demands. Again this is debatable. Chronic patients are more emergency-prone than healthy people. Emergencies may also be correlated. A massive accident can result in several calls. o There are instants in which the frequency of calls is higher than in others. This defines the nonstationary property of the demand function. • Travel times from the base to emergency sites are relatively homogeneous. Bases are geographically located and ambulances are dispatched from bases, or diverted from the road, so to assure patients will be reached promptly. Table below shows standards and observed waiting times reported in the literature. Standards are not only concerned with average values, but also with the tail of the distribution. CITY AREA STANDARD OBSERVED Ravi Nagar 50% under 8’ 75% under 8’ (Population : 5,00,000) 95% under

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