Kendall’s notation is a system used to describe the characteristics of queueing systems in operations research and queuing theory. It’s named after the statistician David G. Kendall, who contributed significantly to the field. The notation is typically written as A/B/C, where each letter represents a specific aspect of the queueing system. Here's a breakdown of what each component signifies:
1. A (Arrival Process): Describes the statistical distribution of arrival times. Common notations include:
• M: Markovian (Poisson process), where arrivals follow an exponential distribution.
• G: General distribution, where arrivals follow any general distribution.
• D: Deterministic, where arrivals occur at fixed intervals.
• E: Erlang distribution, which is a special case of the Gamma distribution.
2. B (Service Time Distribution): Describes the statistical distribution of service times. Common notations include:
• M: Markovian (exponential distribution), indicating that service times are exponentially distributed.
• G: General distribution, where service times follow any general distribution.
• D: Deterministic, where service times are fixed.
• E: Erlang distribution, which is a specific case of the Gamma distribution.
3. C (Number of Servers): Indicates the number of parallel servers in the queue. For example:
• 1: Single server.
• 2: Two servers.
• ∞: Infinite number of servers, which corresponds to a system where there is no waiting time (like a multi-channel system where all requests are serviced instantly).
So, for example, an M/M/1 queue represents a system with a Poisson arrival process, exponential service times, and a single server. If you see M/G/2, it means Poisson arrivals, general service time distribution, and two servers.
This notation helps in analyzing and comparing different queueing models, providing insights into their performance and efficiency.
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