M/D/1 queue: Difference between revisions

Revision as of 20:09, 24 July 2016

Revision as of 22:47, 30 August 2016

Line 94:

The transient solution of an M/D/1 queue of finite capacity N, often written M/D/1/N, was published by Garcia et al in 2002.<ref>{{cite journal | last1 = Garcia | first1 = Jean-Marie | last2 = Brun | first2 = Olivier | last3 = Gauchard | first3 = David | year = 2002 | title = Transient Analytical Solution of M/D/1/N Queues | journal = Journal of Applied Probability | volume = 39 | issue = 4 | pages = 853–864 | publisher = Applied Probability Trust | jstor = 3216008}}</ref>

The mean number of customers in M/D/1/N queue presented in Garcia et al. 2002 is as follows:

<math>X_N=N-\frac{\sum_{k=0}^{N-1}b_k}{1+\rho b_{N-1}};

</math>

The mean waiting time W_N in the M/D/1/N queuing system presented in Garcia et al. 2002 is as follows:

<math>W_N=(N-1-\frac{\sum_{k=0}^{N-1}b_k-N}{\rho b_{N-1}})T</math>

==Application==