What is Kendalls notation?
Kendalls notation is a notation system used to describe the characteristics of queuing systems, which are systems that involve waiting in a queue for service.
The notation system was first introduced by David George Kendall in 1953 and is widely used in the field of operations research and queueing theory.
list of Kendalls notation symbols:
Symbol | Meaning |
A | Arrival process |
B | Service time distribution |
C | Number of servers |
D | Queue discipline |
E | System capacity |
F | Population size |
G | General distribution |
H | Holding cost |
J | Job size |
K | Capacity constraint |
M | Markovian arrival process |
N | Number of customers |
O | Order of service |
P | Priority rule |
Q | Queue size limit |
R | Service rate |
S | Service time |
T | Think time |
U | Utilization |
V | Visit order |
W | Wait time |
X | Offered load |
Y | Service node |
Z | Think time distribution |
- Kendalls notation is a standardized way of representing queuing systems, and these symbols provide a shorthand way to describe the important features of a queuing system.
- By using Kendalls notation, analysts can communicate the key parameters of a queuing system quickly and efficiently.
- Kendalls notation consists of a set of symbols that describe the key characteristics of a queuing system, including the number of servers, the queueing discipline, and the arrival and service distributions.
The notation is written as A/S/m/K/N/D, where:
- A represents the arrival process of customers to the system. It can be described using symbols such as M for a Poisson process or G for a general distribution.
- S represents the service process of customers in the system. It can be described using symbols such as M for an exponential distribution or G for a general distribution.
- m represents the number of servers in the system.
- K represents the maximum number of customers that can be in the system, including those waiting in the queue.
- N represents the number of customers in the system.
- D represents the queueing discipline or the order in which customers are served. Common symbols include FCFS (first-come, first-served), LCFS (last-come, first-served), and PS (priority service).
Kendalls notation provides a concise and standardized way of describing the characteristics of queuing systems, which is useful for communication and comparison between different systems.
It is widely used in research and practice to study the behavior of queuing systems and to make informed decisions about their design and operation.
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