Characteristics of queuing models in operational research
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Primary Queuing Model Characteristics
The characteristics that comprise a queuing model are mentioned below. Each characteristic is represented through a single letter that is mentioned within brackets:
Request Arrival Rate (a) – A service request normally arrives through one of the four patterns viz. steady, irregular, regular or random.
Service Distribution Rate (s) – It involves the number of requests that are processed within a given time period.
Utilization (u) – It is about the traffic intensity that is determined by dividing the request arrival rate with the service rate.
Number of Servers (c) – It is about the total number of servers that have been employed to process the queue request. The length of a line elongates or shortens as per the total number of tellers that are available on duty.
Queue Discipline – The standard deviation calculation is affected by how queued requests are processed.
Variables in Queuing Model Formulae
While the primary queuing model characteristics remain the same in a model formulae, there are variables too that could be put to use as per the requirements of a queuing model. The list of variables comprises the following:
Average number of waiting requests (w)
Average number in the system (S)
Average waiting time (Tw)
Average time in system, i.e., response time (Ts)
Delay due to queuing (D)
Number of requests or clients (K)
Probability that all servers are busy (P(c))
Probability that there are K requests in the system (P(K))
Probability that there is no delay (P(0))
Erlang-B (B(c,U))
Erlang-C (C(c,U))
Erlang moment (m)
In order to calculate these values, the formulae that are used depend on type of distribution and the type of queue. The use of these values increases in the case of more complex queues like a multiple server queue.
The characteristics that comprise a queuing model are mentioned below. Each characteristic is represented through a single letter that is mentioned within brackets:
Request Arrival Rate (a) – A service request normally arrives through one of the four patterns viz. steady, irregular, regular or random.
Service Distribution Rate (s) – It involves the number of requests that are processed within a given time period.
Utilization (u) – It is about the traffic intensity that is determined by dividing the request arrival rate with the service rate.
Number of Servers (c) – It is about the total number of servers that have been employed to process the queue request. The length of a line elongates or shortens as per the total number of tellers that are available on duty.
Queue Discipline – The standard deviation calculation is affected by how queued requests are processed.
Variables in Queuing Model Formulae
While the primary queuing model characteristics remain the same in a model formulae, there are variables too that could be put to use as per the requirements of a queuing model. The list of variables comprises the following:
Average number of waiting requests (w)
Average number in the system (S)
Average waiting time (Tw)
Average time in system, i.e., response time (Ts)
Delay due to queuing (D)
Number of requests or clients (K)
Probability that all servers are busy (P(c))
Probability that there are K requests in the system (P(K))
Probability that there is no delay (P(0))
Erlang-B (B(c,U))
Erlang-C (C(c,U))
Erlang moment (m)
In order to calculate these values, the formulae that are used depend on type of distribution and the type of queue. The use of these values increases in the case of more complex queues like a multiple server queue.
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