Simulation and Modelling > Introduction > What is a single server queuing system?

Single Server Queuing System:

Consider a service station in which customers arrive in accordance with a nonhomogeneous Poisson process with intensity function λ(t) t>=0. There is a single server, and upon arival a customer either enters service if the server is free at that moment or else wait in a queue (line).

When the server completes serving a customer, it then either begins serving the the customer that had been waiting the longest, or , if there are no waiting customers, it remains free untill the next customr's arrival. The amount of time it takes to service a customer is a random variable having probability distribution. In addition, there is a fixed time T after which no additional arrivals are allowed to enter the system. It is also called FIFO single-server model.

 

 

In case of Next-event time advance for the single-server queue, let us consider the following notation:

t₁ = time of arrival of i-th customer (t ₀)

A_i = t_i - t_i-1 = interarrival time between (i-1)^th and i ^th customers (usually assumed to be a random variable from some probability distribution)
S_i = service-time requirement of i-th customer (another random variable)
D_i = delay in queue of i-th customer
C_i = t_i + D_i + S_i = time i-th customer completes service and departs
e_j = time of occurrence of the j-th event (of any type), j = 1, 2, 3, …

 

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