Sensitivity analysis and simulation of a multiserver queueing system with mixed service time distribution

The motivation of mixing distributions in communication/queueing systems modeling is that some input data (e.g., service time in queueing models) may follow several distinct distributions in a single input flow. In this paper, we study the sensitivity of performance measures on proximity of the service time distributions of a multiserver system model with two-component Pareto mixture distribution of service times. The theoretical results are illustrated by numerical simulation of the M/G/c systems while using the perfect sampling approach

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"

Energy-Aware Queueing Models and Controls for Server Farms

Data centers are known to consume substantial amounts of energy. Together with the rising cost of energy, this has created a major concern. Server farms, being integral parts of data centers, waste energy while they are idle. Turning idle servers off may appear to eliminate this wastage. However, turning the server back on at the arrival of the next service request incurs a setup cost in the form of additional delays and energy consumption. Thus, a careful analysis is required to come up with the optimal server control policy. In this thesis, a queueing theoretic analysis of single server systems is carried out to determine optimal server control policies. Additionally, multiple server systems are also be studied through numerical methods. In this case, the task assignment policies that define how incoming requests are routed among the servers are also studied along with the control policies. The results of this study illustrate that the optimal control policy for a single server system leaves an idle server on or switches it off immediately when there is no request to serve. This is a general result that does not depend on service, setup and idling time distributions. However, in the case of multiserver systems, there is a plethora of choices for task assignment and server control policies. Our study indicates that the combination of the Join the Shortest Queue and Most Recently Busy task assignment policies can save up to 30% of the system cost if the control policy applied can wait for a specific amount of time before turning a server off. Moreover, a similar gain can be achieved by the simple Join the Shortest Queue task assignment policy when it is used along with a control policy that leaves an optimized number of servers on while switching the remaining servers off when they become idle

Exact Simulation Techniques in Applied Probability and Stochastic Optimization

This dissertation contains two parts. The first part introduces the first class of perfect sampling algorithms for the steady-state distribution of multi-server queues in which the arrival process is a general renewal process and the service times are independent and identically distributed (iid); the first-in-first-out FIFO GI/GI/c queue with 2 <= c < 1. Two main simulation algorithms are given in this context, where both of them are built on the classical dominated coupling from the past (DCFTP) protocol. In particular, the first algorithm uses a coupled multi-server vacation system as the upper bound process and it manages to simulate the vacation system backward in time from stationarity at time zero. The second algorithm utilizes the DCFTP protocol as well as the Random Assignment (RA) service discipline. Both algorithms have finite expected termination time with mild moment assumptions on the interarrival time and service time distributions. Our methods are also extended to produce exact simulation algorithms for Fork-Join queues and infinite server systems. The second part presents general principles for the design and analysis of unbiased Monte Carlo estimators in a wide range of settings. The estimators possess finite work-normalized variance under mild regularity conditions. We apply the estimators to various applications including unbiased steady-state simulation of regenerative processes, unbiased optimization in Sample Average Approximations and distribution quantile estimation

Exact Results for the Distribution of the Partial Busy Period for a Multi-Server Queue

Exact explicit results are derived for the distribution of the partial busy period of the M/M/c multi-server queue for a general number of servers. A rudimentary spectral method leads to a representation that is amenable to efficient numerical computation across the entire ergodic region. An alternative algebraic approach yields a representation as a finite sum of Marcum Q-functions depending on the roots of certain polynomials that are explicitly determined for an arbitrary number of servers. Asymptotic forms are derived in the limit of a large number of servers under two scaling regimes, and also for the large-time limit. Connections are made with previous work. The present work is the first to offer tangible exact results for the distribution when the number of servers is greater than two

Stability Problems for Stochastic Models: Theory and Applications II

Most papers published in this Special Issue of Mathematics are written by the participants of the XXXVI International Seminar on Stability Problems for Stochastic Models, 21­25 June, 2021, Petrozavodsk, Russia. The scope of the seminar embraces the following topics: Limit theorems and stability problems; Asymptotic theory of stochastic processes; Stable distributions and processes; Asymptotic statistics; Discrete probability models; Characterization of probability distributions; Insurance and financial mathematics; Applied statistics; Queueing theory; and other fields. This Special Issue contains 12 papers by specialists who represent 6 countries: Belarus, France, Hungary, India, Italy, and Russia