arXiv subjects
Publications and source records attributed to Myron Hlynka.
We propose a new queueing model, motivated by the phenomenon of pseudoprogression in cancer, in which the length of a queue appears to increase initially, before reducing to a steady state. We assume that servers arrive to the queue alongside the customers, i.e. `disguised' as customers. We derive the general equations for this model using matrix analytic methods, and demonstrate its behaviour with numerical simulations.
The probabilistic interpretation of Laplace transforms is used to help to describe the Laplace Transform $L(s)$ of improper random variables. In particular, busy periods in queueing models are examined. The value of $L(0)$ is explained in certain special cases.
The choice of forward and reverse parking in a parking lot is studied as a stochastic process. An $M/M/c/c$ queueing system is used as an initial framework. We use Monte Carlo simulation to get the relationship between vehicle orientation and vehicle entry and exit rates, as well as the most likely parking states at each specific rate. We view the change in parking status over time.
Vacation queueing systems are widely used as an extension of the classical queueing theory. We consider both working vacations and regular vacations in this paper, and compare systems with vacations to the regular $M/M/1$ system via mean service rates and expected numbers of customers, using matrix-analytic methods.
Scheduling service order, in a very specific queueing/inventory model with perishable inventory, is considered. Different strategies are discusses and results are applied to the tragic cave situation in Thailand in June and July of 2018.
We use probability urn models to discover some known and unknown series identities involving Fibonacci numbers.
A special customer must complete service from two servers in series, in either order, each with an M/M/1 queueing system. It is assumed that the two queueing system lengths are independent with initial numbers of customers a and b at the instant when the special customer arrives. We find the expected total time (ETT) for the special customer to complete service. We show that even if the interarrival and service time parameters of two queues are identical, there exist examples (specific values of the parameters and initial lengths) for which the special customer surprisingly has a lower expected total time to completion by joining the longer queue first rather than the shorter one.