Queuing System Research Paper
To describe a queuing system,
An input process and an output process must be specified.
Some examples of input and output processes are given below
Situation Input Process Output Process
Bank Customers arrive at bank Tellers serve the customers
Pizza parlor Requests for pizza delivery Pizza parlor sends out are received truck to deliver pizzas
Hospital blood bank Pints of blood arrive Patients use up pints of blood
Naval shipyard Ships at sea break down Ships are repaired and
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In most cases, we assume that the service time distribution is independent of the number of customers present. This implies, for example, that the server does not work faster when more customers are present.
Modelling Arrival and Service Processes
The Kendall–Lee Notation for Queuing Systems
Each queuing system is described by six characteristics:
The first characteristic specifies the nature of the arrival process.
M Interarrival times are independent, identically distributed (iid) random variables having an exponential distribution.
D Interarrival times are iid and deterministic.
Ek Interarrival times are iid Erlangs with shape parameter k.
GI Interarrival times are iid and governed by some general distribution.
The second characteristic specifies the nature of the service times:
M Service times are iid and exponentially distributed.
D Service times are iid and deterministic.
Ek Service times are iid Erlangs with shape parameter k.
G Service times are iid and follow some general distribution.
The third characteristic is the number of parallel
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The company is deciding whether or not it is worthwhile to hire (at $4 per hour) a helper for the clerk.
If the helper is hired, the clerk will take an average of only 4 minutes to process requests for tools. Assume that service and interarrival times are exponential. Should the helper be hired? Solution:
Problems in which a decision maker must choose between alternative queuing systems are called queuing optimization problems. In the current problem, the company’s goal is to minimize the sum of the hourly service cost and the expected hourly cost due to the idle times of machinists. In queuing optimization problems, the component of cost due to customers waiting in line is referred to as the delay cost.
The queuing formula L = lamda* W is very general and can be applied to many situations that do not seem to be queuing problems. Think of any situation where a quantity (such as mortgage loan applications, potatoes at McDonald’s, revenues from computer sales) flows through a system. If we let
L = average amount of quantity present
Lamda = rate at which quantity arrives at system
W = average time a unit of quantity spends in system
then L = Lamda * W
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