Queueing

The mathematical field whose major result is enraging you about call centres

June 4, 2015 — April 6, 2020

Not much to say right now, except that I always forget the name of the useful tool from queuing theory, Kingman’s approximation for waiting time.

\[ \mathbb {E} (W_{q})\approx \left({\frac {\rho }{1-\rho }}\right)\left({\frac {c_{a}^{2}+c_{s}^{2}}{2}}\right)\tau \] where τ is the mean service time (i.e. μ = 1/τ is the service rate), λ is the mean arrival rate, ρ = λ/μ is the utilization, \(c_a\) is the coefficient of variation for arrivals (that is the standard deviation of arrival times divided by the mean arrival time) and \(c_s\) is the coefficient of variation for service times.

1 References

Glasserman, Heidelberger, Shahabuddin, et al. 1999. Multilevel Splitting for Estimating Rare Event Probabilities.” Operations Research.
Kingman. 1961. The Single Server Queue in Heavy Traffic.” Mathematical Proceedings of the Cambridge Philosophical Society.
Vázquez, Oliveira, Dezsö, et al. 2006. Modeling Bursts and Heavy Tails in Human Dynamics.” Physical Review E.