Simulation and Modelling - Old Questions
9. Define traffic intensity and server utilization. Write down the Kendall’s notation for queuing system with example.
Traffic Intensity
The ratio of the mean service time to the mean inter arrival time is called traffic intensity. I.e. u= λ"Ts or u=Ts/Ta
Server Utilization
Server utilization is the percentage of the time that all servers are busy. Server utilization factor (ρ ) is the ratio of average arrival rate (λ) to the average service rate (μ).
ρ = λ/μ in the case of a single server model
ρ = λ/μn in the case of a “n” server model
Kendall's notation
Kendall’s notation is used for parallel server systems. The basic format of this notation is of form: A / B / c / N / K, where, A, B, c, N, K respectively indicate arrival pattern, service pattern, number of servers, system capacity, and Calling population.
The symbols used for the probability distribution for inter arrival time, and service time are, D for deterministic, M for exponential (or Markov) and Ek for Erlang.
E.g.
a) M/D/2/5/∞ stands for a queuing system having exponential arrival times, deterministic service time, 2 servers, capacity of 5 customers, and infinite population.
b) M/D/2 means exponential arrival time, deterministic service time, 2 servers, infinite service capacity, and infinite population.