Queuing problems

In several chapters we discussed how the quality of the analytical result defines the amount of information which is obtained on a sampled system. Obvious quality criteria are accuracy and precision. An equally important criterion is the analysis time. This is particularly true when dynamic systems are analyzed. For instance a relationship exists between the measurability and the sampling rate, analysis time and precision (see Chapter 20). The monitoring of environmental and chemical processes are typical examples where the management of the analysis time is 

In this section waiting and queues are discussed in order to provide some basic understanding of general queuing behaviour, in particular in analytical laboratories. This should allow a qualitative forecast of the effect of managerial decisions. 

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In Section 42.2 we have discussed that queuing theory may provide a good qualitative picture of the behaviour of queues in an analytical laboratory. However the analytical process is too complex to obtain good quantitative predictions. As this was also true for queuing problems in other fields, another branch of Operations Research, called Discrete Event Simulation emerged. The basic principle of discrete event simulation is to generate sample arrivals. Each sample is characterized by a number of descriptors, e.g. one of those descriptors is the analysis time. In the jargon of simulation software, a sample is an object, with a number of attributes (e.g. analysis time) and associated values (e.g. 30 min). Other objects are e.g. instruments and analysts. A possible attribute is a list of the analytical... 

Suppose a random set of dots representing a sequence of events is given. The following question may be asked. If I start observing at some time t0, how long do I have to wait for the next event to occur Of course, the time 6 from t0 to the next event is a random variable with values in (0, oo) and the quantity of interest is its probability density, w(6 t0) (which depends parametrically on t0 unless the random set of events is stationary). This question is of particular interest in queuing problems. The function w(6 t0) has also been measured electronically for the arrivals of photons produced by luminescence. 

The sizes of the units in the system are calculated using a the Queuing Multi Objective Optimizer (qmoo) developed at the Energy Systems Laboratory at the EPFL (Leyland [3]) in combination with a linear programming problem as described by in Weber et al. [2]. The sizes of the units considered are shown on Table 1. 

In the real world, a call center is more complicated with multi-tasks and the diversify of client needs. The process also has become increasingly difficult since internal and external variables are to be added. Thus, in order to improve call center performances, the prospect research should more concern several aspects in call center optimizations, forecasting method, for example, more complex of the queuing model, routing problem, staff scheduling problems, multi-skill scheduling, and real-time adherence. 

Transportation Research, Part B Methodological (0191-2615). Scope Development and solution to problems, particularly those such as traffic flow, analysis of transportation networks, and queuing theory that require mathematical analysis. 

Cohen, J.W. and O.J. Boxma (1983), "Boundary Value Problems in Queuing System Analysis", North-Holland, Amsterdam. 

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