The effect of queue size on the throughput, in group failure mode, for the loaded transport channel

The external data flow decreases the throughput of the transport connection. The indicator of this external load is the queue size in front of the protocol data. In this article, using a mathematical model in analytical and numerical forms, the relation between the throughput of the channel and the protocol parameters are presented including the queue size parameter. In this work the effect of the queue size on time-out duration has been shown, which is one of the important parameters and it’s studied weakly in researches. Also, the relation between round-trip delay, the reliability of the transmission of the information segments with queue size are also shown.

Study on Transient Queue-Size Distribution in the Finite-Buffer Model with Batch Arrivals and Multiple Vacation Policy

The transient behavior of the finite-buffer queueing model with batch arrivals and generally distributed repeated vacations is analyzed. Such a system has potential applications in modeling the functioning of production systems, computer and telecommunication networks with energy saving mechanism based on cyclic monitoring the queue state (Internet of Things, wireless sensors networks, etc.). Identifying renewal moments in the evolution of the system and applying continuous total probability law, a system of Volterra-type integral equations for the time-dependent queue-size distribution, conditioned by the initial buffer state, is derived. A compact-form solution for the corresponding system written for Laplace transforms is obtained using an algebraic approach based on Korolyuk’s potential method. An illustrative numerical example presenting the impact of the service rate, arrival rate, initial buffer state and single vacation duration on the queue-size distribution is attached as well.

Queue Size Distribution on a New ND Policy Geo/G/1 Queue and Its Computation Designs

This paper examines a new ND policy in the discrete-time Geo/G/1 queue. Under this ND policy, the idle server restarts its service when the N and D policies are simultaneously satisfied. By two classifications of the customers, the probability-generating function and the probabilistic analysis, the steady-state queue size distributions at a departure time and an arbitrary time t + are studied. Finally, the theoretical results are applied to the power-saving problem of a wireless sensor network. To improve model universality and numerical slowness, some computation designs are carried out. Under the N, D, and two ND policies, the numerical experiments are presented to obtain the optimal policy thresholds and the corresponding minimum power consumptions are compared.

QLREDActive Queue Management Algorithm

The Random Early Detection (RED) algorithm has not been successful in keeping the average queue size low. In this paper, we an improved RED-based algorithm called QLRED which divides the dropping probability function of the RED algorithm into two equal segments. The first segment utilises a quadratic packet dropping function while the second segment deploys a linear packet dropping function respectively so as to distinguish between light and high traffic loads. The ns-3 simulation performance evaluations clearly showed that QLRED algorithm effectively controls the average queue size under various network conditions resulting in a low delay. Replacing/upgrading the RED algorithm in Internet routers requires minimal effort since only the packet dropping probability profile needs to be adjusted.

Active Queue Management in RED Considering Critical Point on Target Queue

The basic philosophy behind RED is to prevent congestion. When the average queue length exceeds the minimum threshold, packets are randomly dropped, or the explicit congestion notification bit is marked. Since network requirements differ significantly, it is not an optimal approach to establish RED parameters with constant value. There is a new algorithm we are proposing called Critical Point on Target Queue (AQM-RED-CPTQ), provide greater congestion management over the network while also preserving the value of RED. To overcome the problem in RED without changing queue weight parameter, we have proposed few models to control the congestion by introducing range parameter with probability and control mechanism which will belong between minimum and maximum threshold. The current queue size is controlled together with average queue size. A new range variable has been introduced to improve the performance of priority queue of existing RED based algorithm which improves the overall performance of networks. For each packet, minimum and maximum threshold has been updated and dropped with probability (Pa) for a special condition. Instead of multiplicative increase and decrease the maximum probability, the scheme uses additive-increase and multiplicative-decrease. Once the AVG queue length is close to the minimum threshold value, our approach automatically sets queue parameter according to queue conditions and handles queuing delay and improve throughput. The simulated results proof that our approaches are better than RED in terms of throughput, end to end delay, packet delivery ratio and goodput.

Optimal Profit Analysis of Machine Repair Problem with Repair in Phases and Organizational Delay

In this article, we study machine repair problems (MRP) consisting of the finite number of operating machines with the provisioning of the finite number of warm standby machines under the care of a single unreliable server. For the machining system’s uninterrupted functioning, an operating machine is immediately replaced with the available warm standby machine in negligible switchover time whenever it fails. The concept of threshold vacation policy: N-policy is also considered. Under this vacation policy, the server starts to serve the failed machines on the accumulation of a pre-specified number of failed machines in the system. The server continues until the system is empty from the failed machines; after that, the server goes for vacation. The notion of an organizational delay, server breakdown, and repair in multiple phases is also conceptualized to build the studied model more realistic. The recursive matrix method is used to find steady-state queue size distribution, and subsequently, various system performance measures are also developed to validate the studied model. The optimal analysis has been performed to identify the critical design parameters for the governing model. The state-of-the-art of the present study is its mathematical modeling of the multi-machine stochastic problem with varied limitations and strategies. The methodology to obtain queue size distribution, optimal design parameters, is beneficial for dealing with other complex and sophisticated real-time machining problems in the service system, computer and communication system, manufacturing and production system, etc. The present problem is limited to fewer machines, which can be extended to more machines with different topologies with high computational facilities.

Improved queue-size scaling for input-queued switches via graph factorization

This paper studies the scaling of the expected total queue size in an $n\times n$ input-queued switch, as a function of both the load $\rho$ and the system scale n. We provide a new class of scheduling policies under which the expected total queue size scales as $O\big( n(1-\rho)^{-4/3} \log \big(\!\max\big\{\frac{1}{1-\rho}, n\big\}\big)\big)$, over all n and $\rho<1$, when the arrival rates are uniform. This improves on the best previously known scalings in two regimes: $O\big(n^{1.5}(1-\rho)^{-1} \log \frac{1}{1-\rho}\big)$ when $\Omega\big(n^{-1.5}\big) \le 1-\rho \le O\big(n^{-1}\big)$ and $O\big(\frac{n\log n}{(1-\rho)^2}\big)$ when $1-\rho \geq \Omega(n^{-1})$. A key ingredient in our method is a tight characterization of the largest k-factor of a random bipartite multigraph, which may be of independent interest.