AppelMalade

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Appel Malade
Vaulx-en-Velin, France
Appel Malade installs, maintains and repairs nurse call systems for nursing homes, hospitals, clinics, rehabilitation centres and senior residences in France. The company designs communication solutions between caregivers and patients: intercoms, call buttons, light and sound signalling and centralised alarm management.

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Nurse call systems in care homes and hospitals are a good example of a real multi-server queue: calls arrive at random, several caregivers act as servers, and the key figure is the probability that a call has to wait. A common starting point is the M/M/c model, where arrivals follow a Poisson process and service times are exponential. The Erlang C formula gives the probability of waiting, and in Maple it can be written directly with a sum and a factorial, then used in a simple loop to find the smallest number of servers that meets a target waiting probability. One frequent mistake is to forget that the offered load must stay below the number of servers, otherwise the queue has no steady state. Another is to assume exponential service times when real intervention durations are much more variable, so a simulation built with the Statistics package is a useful cross-check. I would be interested to hear how others here compare analytic queueing results with Monte Carlo simulation in Maple, in particular when some calls have priority, such as emergency alarms.

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