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Problem Definition (Wiki)

In queuing theory, a discipline within the mathematical theory of probability, an M/M/1 queue represents the queue length in a system having a single server, where arrivals are determined by a Poisson process and job service times have an exponential distribution. The model name is written in Kendall’s notation. The model is the most elementary of queuing models and an attractive object of study as closed-form expressions can be obtained for many metrics of interest in this model. An extension of this model with more than one server is the M/M/c queue.

O2DES.Net

(1) Statics, which describes what is to be simulated, and encapsulates all entities that are to be referred to, but not altered throughout the stochastic process in the simulation run. For example, we can define the terminal layout and vessel type as the static entity as they are not expected to change.

(2) Dynamics, which is used to capture the changing properties of the simulation run, i.e., properties related to the sample path, and take snapshots of the status which are subjected to change with the simulation clock, with static properties described in the static entities. For example, vessel arrivals and departures, and the storage volume changes from time to time, they will be defined as a dynamic entity.

(3) Events, which is the control logic behind DES and describes how the system operates in the real world. Events are invoked at discrete time points, and changes the properties of the dynamic entities. For example, when a vessel arrives, a berthing event will be triggered by the vessel and then a discharging event will follow after.

mm1_o2des

Static

mm1_static1
mm1_static2

Dynamic

mm1_dynamic1
mm1_dynamic3
mm1_dynamic2

Event

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Simulator

mm1_sim1

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mm1_sim3
mm1_sim2