# Lee Jones - University of Massachusetts at Lowell

**Starts:**4:00 pm on Thursday, November 1, 2012

**Ends:**5:00 pm on Thursday, November 1, 2012

**Location:**MCS 148

Title: Order statistics probability rates and some new results for statistical inference from transactional data in queuing systems. Abstract: Efficient algorithms were initially developed for computing the probability that the order statistics of
n i.i.d. uniform random variables lie in a given n-dimensional rectangular region in order to calculate
the cumulative distribution of the Kolmogorov statistic. These algorithms were rediscovered and used
to find expected queue length (and other queue performance measures) in a queuing system from the
set of recorded start/stop service data in a time interval in the interior of which each server who became free was immediately reengaged by a waiting customer. With most practical data there are time gaps between the recorded service completion and the recorded start of service with a waiting customer. These may be due to customer delay in engaging a free server , to server delay in availability to the next in queue, or to both. We propose models for the various delays . By generalizing the order statistics probability computational problem and developing feasible algorithms for its solution we can give confidence intervals for queue performance measures for practical transactional data.