Stabilization of an overloaded queueing network using measurement-based admission control

Admission control can be employed to avoid congestion in queueing networks subject to overload. In distributed networks the admission decisions are often based on imperfect measurements on the network state. This paper studies how the lack of complete state information affects the system performance by considering a simple network model for distributed admission control. The stability region of the network is characterized and it is shown how feedback signaling makes the system very sensitive to its parameters.Comment: Published at http://dx.doi.org/10.1239/jap/1143936256 in the Journal of Applied Probability (http://projecteuclid.org/jap) by the Applied Probability Trust (http://www.appliedprobability.org/

Survey of traffic control schemes and error control schemes for ATM networks

Among the techniques proposed for B-ISDN transfer mode, ATM concept is considered to be the most promising transfer technique because of its flexibility and efficiency. This paper surveys and reviews a number of topics related to ATM networks. Those topics cover congestion control, provision of multiple classes of traffic, and error control. Due to the nature of ATM networks, those issues are far more challenging than in conventional networks. Sorne of the more promising solutions to those issues are surveyed, and the corresponding results on performance are summarized. Future research problems in ATM protocol aspect are also presented

Coupling and monotonicity of queueing processes

The main purpose of this work is to give a survey of main monotonicity properties of queueing processes based on the coupling method. The literature on this topic is quite extensive, and we do not consider all aspects of this topic. Our more concrete goal is to select the most interesting basic monotonicity results and give simple and elegant proofs. Also we give a few new (or revised) proofs of a few important monotonicity properties for the queue-size and workload processes both in single-server and multi- server systems. The paper is organized as follows. In Section 1, the basic notions and results on coupling method are given. Section 2 contains known coupling results for renewal processes with focus on construction of synchronized renewal instants for a superposition of independent renewal processes. In Section 3, we present basic monotonicity results for the queue-size and workload processes. We consider both discrete-and continuous-time queueing systems with single and multi servers. Less known results on monotonicity of queueing processes with dependent service times and interarrival times are also presented. Section 4 is devoted to monotonicity of general Jackson-type queueing networks with Markovian routing. This section is based on the notable paper [17]. Finally, Section 5 contains elements of stability analysis of regenerative queues and networks, where coupling and monotonicity results play a crucial role to establish minimal suficient stability conditions. Besides, we present some new monotonicity results for tandem networks

A tandem queue with server slow-down and blocking

We consider two variants of a two-station tandem network with blocking. In both variants the first server ceases to work when the queue length at the second station hits a `blocking threshold'. In addition, in variant $2$ the first server decreases its service rate when the second queue exceeds a `slow-down threshold', which is smaller than the blocking level. In both variants the arrival process is Poisson and the service times at both stations are exponentially distributed. Note, however, that in case of slow-downs, server $1$ works at a high rate, a slow rate, or not at all, depending on whether the second queue is below or above the slow-down threshold or at the blocking threshold, respectively. For variant $1$, i.e., only blocking, we concentrate on the geometric decay rate of the number of jobs in the first buffer and prove that for increasing blocking thresholds the sequence of decay rates decreases monotonically and at least geometrically fast to $\max\{\rho_1,\rho_2\}$, where $\rho_i$ is the load at server $i$. The methods used in the proof also allow us to clarify the asymptotic queue length distribution at the second station. Then we generalize the analysis to variant $2$, i.e., slow-down and blocking, and establish analogous results. \u

Control of a tandem queue with a startup cost for the second server

Various systems across a broad range of applications contain tandem queues. Strong dependence between the servers has proven to make such networks complicated and difficult to study. Exact analysis is rarely computationally tractable and sometimes not even possible. Nevertheless, as it is most often the case in reality, there are costs associated with running such systems, and therefore, optimizing the control of tandem queues is of main interest from both a theoretical and a practical point of view. Motivated by this, the present paper considers a tandem queueing network with linear holding costs and a startup cost for the second server. In our work, we present a rather intuitive, easy to understand, and at the same time very accurate technique to approximate the optimal decision policy. Extensive numerical experimentation shows that the approximation works extremely well for a wide range of parameter combinations

Sample-path large deviations for tandem and priority queues with Gaussian inputs

This paper considers Gaussian flows multiplexed in a queueing network. A single node being a useful but often incomplete setting, we examine more advanced models. We focus on a (two-node) tandem queue, fed by a large number of Gaussian inputs. With service rates and buffer sizes at both nodes scaled appropriately, Schilder's sample-path large-deviations theorem can be applied to calculate the asymptotics of the overflow probability of the second queue. More specifically, we derive a lower bound on the exponential decay rate of this overflow probability and present an explicit condition for the lower bound to match the exact decay rate. Examples show that this condition holds for a broad range of frequently used Gaussian inputs. The last part of the paper concentrates on a model for a single node, equipped with a priority scheduling policy. We show that the analysis of the tandem queue directly carries over to this priority queueing system.Comment: Published at http://dx.doi.org/10.1214/105051605000000133 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

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"

An approximation approach for the deviation matrix of continuous-time Markov processes with application to Markov decision theory

We present an update formula that allows the expression of the deviation matrix of a continuous-time Markov process with denumerable state space having generator matrix Q* through a continuous-time Markov process with generator matrix Q. We show that under suitable stability conditions the algorithm converges at a geometric rate. By applying the concept to three different examples, namely, the M/M/1 queue with vacations, the M/G/1 queue, and a tandem network, we illustrate the broad applicability of our approach. For a problem in admission control, we apply our approximation algorithm toMarkov decision theory for computing the optimal control policy. Numerical examples are presented to highlight the efficiency of the proposed algorithm. © 2010 INFORMS