We consider an M/G/1 queue in which the customers, while waiting in line, may renege from it. We show the Nash equilibrium profile among customers and show that it is defined by two sequences of thresholds. For each customer, the decision is based on the observed past (which determines from what sequence the threshold is taken) and the observed queue length (which determines the appropriate element in the chosen sequence). We construct a set of equations that has the Nash equilibrium as its solution and discuss the relationships between the properties of the service time distribution and the properties of the Nash equilibrium, such as uniqueness and finiteness.
We propose a method to analyze M/G/1/m queuing systems with the function of random dropping of customers and service time distribution dependent on the queue length. We obtain formulas to determine the Laplace transforms of the distribution of the number of customers in the system during busy period and of the distribution function of the busy period and to calculate the stationary characteristics. The relations for the stationary characteristics are tested using simulation models constructed with the use of the GPSS World tools. The results of the use of various control tools of system parameters are compared in the example.
In this paper we describe a perfect simulation algorithm for the stable M/G/c queue. Sigman (2011) showed how to build a dominated coupling-from-the-past algorithm for perfect simulation of the super-stable M/G/c queue operating under first-come-first-served discipline. Sigman's method used a dominating process provided by the corresponding M/G/1 queue (using Wolff's sample path monotonicity, which applies when service durations are coupled in order of initiation of service). The method exploited the fact that the workload process for the M/G/1 queue remains the same under different queueing disciplines, in particular under the processor sharing discipline, for which a dynamic reversibility property holds. We generalise Sigman's construction to the stable case by comparing the M/G/c queue to a copy run under random assignment. This allows us to produce a naive perfect simulation algorithm based on running the dominating process back to the time it first empties. We also construct a more efficient algorithm that uses sandwiching by lower and upper processes constructed as coupled M/G/c queues started respectively from the empty state and the state of the M/G/c queue under random assignment. A careful analysis shows that appropriate ordering relationships can still be maintained, so long as service durations continue to be coupled in order of initiation of service. We summarise statistical checks of simulation output, and demonstrate that the mean run-time is finite so long as the second moment of the service duration distribution is finite.
We consider the loss probability in the stationary M/G/1+G queue, i.e., the stationary M/G/1 queue with impatient customers whose impatience times are generally distributed. It is known that the loss probability is given in terms of the probability density function v(x) of the virtual waiting time and that v(x) is given by a formal series solution of a Volterra integral equation. In this paper, we show that the series solution of v(x) can be interpreted as the probability density function of a random sum of dependent random variables and we reveal its dependency structure through the analysis of a last-come first-served, preemptive-resume M/G/1 queue with workload-dependent loss. Furthermore, based on this observation, we show some properties of the loss probability.
This article presents the letters sent by the late nineteenth-century English writer Elizabeth Mayhew Edmonds to the Greek folklorist Nikolaos G. Politis. While a preoccupation with folklore and ethnology predisposed the Victorian public to take a narrow view of Greek society, Edmonds's interest in both vernacular culture and the literary, social and political life of modern Greece enriched the complex cultural exchange that developed between European (Neo)Hellenists and Greek scholars. This European-wide discourse promoted modern Greece as an autonomous subject of study, worthy of intellectual pursuit.