The Beauty of a Good Model
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BY MACGREGOR SMITH
INDUSTRIAL ENGINEER – VOLUME 45 NUMBER 2
Modeling transportation and material handling networks is a challenging activity. On the front lines, industrial engineers often use discrete-event simulation to model manufacturing and service systems. But sometimes discrete-event simulation is not the only tools. Occasionally, they can model transportation and material handling networks with analytical models and concepts.
Analytical models of manufacturing and service systems allow one to model the system with fewer variables and parameters, less reliance on random number generators, and more directly with the processes at hand. This article demonstrates useful properties, experiments and applications of a methodology to show that the new state-dependent queue and its networks offer an alternative to discrete-event simulation models.
When dealing with facilities planning and design problems, IEs work to minimize the distances that materials flow in the material handling systems. Analytical modeling is a tool that IEs can use to measure the amount of material flowing through the facility and optimize its path in a way that does not rely on just discrete-event simulation models. Analytical models have the additional advantage of naturally lending themselves to optimization of complex systems that often are more challenging for discrete-event simulation models. Analytical models have uses in areas such as safety engineering, where IEs are concerned with how to evacuate occupants safely from a building or region in case of fires, floods and other natural disasters.
The one of analytical model that we can use is queuing theory. The queuing concept we need to incorporate is termed a state-dependent queue, which has Markovian arrivals (M), general service (G), c-servers (c), and c-capacity (c), or M/G/c/c for short. For example, a person walking along a corridor in the airport enters the corridor, immediately begins service, travels the length of corridor (L), and only slows down when there are increasing numbers of people in the corridor or the width (W) is too restrictive. The corridor has a finite capacity for service equal to the area corridor, or c = L x W. The number of servers equals the capacity. The corridor can be represented as an M/G/c/c queue, but so can parts on a conveyor, vehicles along a highway and so on.
It is a special case of what is called an Erlang loss system. That model is adapted to model physical flows and is termed a “state-dependent” M/G/c/c queue. Adding the state-dependent property extends the concept to other application. So when IEs use the M/G/c/c model, they can dynamically update the speed of all the commodities travelling in the transport mechanism as a function of the density of the number of commodities along the way. One property that makes M/G/c/c model desirable is that they are robust, or insensitive to their input distribution. So even if the input process to the queue is not Markovian, the M/G/c/c queues remain very accurate and appropriate. When adding a new part or process to a discrete-event simulation, IEs must come up with a new simulation model and run repeated simulations to be certain about the results with any level of confidence. Yet a robust analytical model can handle the new part and yield results quickly.
M/G/c/c state-dependent queues are useful for capturing the flow of commodities in transportation and material handling situations with analytical models and provide industrial engineers with new concept and tools in their toolboxes