On M/G/1 system under NT policies with breakdowns, startup and closedown

AbstractThis paper studies the vacation policies of an M/G/1 queueing system with server breakdowns, startup and closedown times, in which the length of the vacation period is controlled either by the number of arrivals during the vacation period, or by a timer. After all the customers are served in the queue exhaustively, the server is shutdown (deactivates) by a closedown time. At the end of the shutdown time, the server immediately takes a vacation and operates two different policies: (i) The server reactivates as soon as the number of arrivals in the queue reaches to a predetermined threshold N or the waiting time of the leading customer reaches T units; and (ii) The server reactivates as soon as the number of arrivals in the queue reaches to a predetermined threshold N or T time units have elapsed since the end of the closedown time. If the timer expires or the number of arrivals exceeds the threshold N, then the server reactivates and requires a startup time before providing the service until the system is empty. If some customers arrive during this closedown time, the service is immediately started without leaving for a vacation and without a startup time. We analyze the system characteristics for each scheme

The Mx/G/1 Queue with Unreliable Server, Delayed Repairs, and Bernoulli Vacation Schedule under T-Policy

In this paper we study a batch arrival queuing system. The server may break down while delivering service. However, repair is not provided immediately, rather it is delayed for a random amount of time. At the end of service, the server may process the next customer if any are available, or may take a vacation to execute some other job. Finally, the server implements the T-policy. We describe for this system an optimal management policy. Numerical examples are provided

Study of feedback queueing system with unreliable waiting server under Multiple Differentiated Vacation Policy

This manuscript analyses a queueing system with Bernoulli schedule feedback of customers, unreliable waiting server under differentiated vacations. The unsatisfied customer may again join the queue with probability α, following Bernoulli schedule. The stationary solution is obtained for the model with aid of Probability Generating function technique. Some important system performance measures are derived and graphical behaviour of these measures with some parameters is analyzed. Finally to obtain the optimal value of service rate for the model, cost optimization is performed through quadratic fit approach

Energy saving policies for a machine tool with warm-up, stochastic arrivals and buffer information

One of the measures for saving energy in manufacturing is the implementation of control strategies that reduces energy consumption during the machine idle periods. Specifically, the paper proposes a framework that integrates different control policies for switching the machine off when the production is not critical, and on either when the part flow has to be resumed or the queue has accumulated to a certain level. A general policy is formalized by modeling explicitly the power consumed in each machine state. A threshold policy is analyzed and the optimal parameter is provided for an M/M/1/K system. Numerical results are based on data acquired with dedicated experimental measurements on a real machining centre, and a comparison with common practices in manufacturing is also reported

Performance improvement of remanufacturing systems operating under N-policy

This thesis deals with N-policy M/G/1 queueing remanufacturing system with general server breakdown and start-up time, where the value of returned products exponentially deteriorates since received. The server will instantly turn on the system, but the system requires a start-up period to prepare for remanufacturing when returned products in the queue reach the value of N. Otherwise, the system keeps in turn-off status. During the remanufacturing process, the machines may break down and will return back to service immediately after repairing. The procedures that will be used to achieve the target are as follows. Firstly, the expression of cost function will be derived and solved. Next, the simulation software ProModel will be used to simulate this problem. Finally, a sensitivity analysis is used on a numerical example to show the applicability of the methodology and quality of results

Some analysis results associated with the optimization problem for a discrete-time finite-buffer NT-policy queue

The prime objective of this paperis to give some analysis results concerning the discrete-time finite-buffer NT-policy queue, which can be utilized to determine the optimal threshold values. By recording the waiting time of the leading customer in server’s vacation period, the model is successfully described as a vector-valued Markov chain. Meanwhile, depending on the special block structure of the one-step transition probability matrix, the equilibrium queue length distribution is calculated through a more effective UL-type RG-factorization. Due to the number of customers served in the busy period does not have the structure of a Galton-Watson branching process, analysis of the regeneration cycle is regarded as a difficult problem in establishing the cost structure of the queueing system. However, employing the concept of i-busy period and some difference equation solving skills, the explicit expression for the expected length of the regeneration cycle is easily derived, and the stochastic decomposition structure of the busy period is also demonstrated. Finally, numerical results are offered to illustrate how the direct search method can be implemented to obtain the optimal management policy.This research was partially supported by grant from NSERC DAS programs, National Natural Science Foundation of China (Nos. 71301111,71171138, 71402072) and the FSUSE (No.2012RC23).http://link.springer.com/journal/123512017-07-30hb201

On transient queue-size distribution in the batch arrival system with the N-policy and setup times

In the paper the $M^{X}/G/1$ queueing system with the $N$-policy and setup times is considered. An explicit formula for the Laplace transform of the transient queue-size distribution is derived using the approach consisting of few steps. Firstly, a "special\u27\u27 modification of the original system is investigated and, using the formula of total probability, the analysis is reduced to the case of the corresponding system without limitation in the service. Next, a renewal process generated by successive busy cycles is used to obtain the general result. Sample numerical computations illustrating theoretical results are attached as well

A Batch Arrival Unreliable Queue with Two Types of General Heterogeneous Service and Delayed Repair under Repeated Service Policy

This paper deals with a single server / / 1 M G X queue under two types of general heterogeneous service with optional repeated service subject to server’s breakdowns and delayed repair. We assume that customers arrive at the system according to a compound Poisson process with rate λ. The server provides two types of general heterogeneous service and a customer has the option to choose any type of service. After the completion of either type of service, the customer has the further option to repeat the same type of service. While the server is working with any types of service or repeated service, it may breakdown at any instant and the service channel will fail for a short interval of time. Furthermore, the concept of delay time is also introduced. We carry out an extensive analysis of this model. Finally, we obtain some important performance measure and reliability indices of this model

Internet Service via Broadband Satellite Networks

The demand for Internet bandwidth has grown rapidly in the past few years. A new generation of broadband satellite constellations promises to provide high speed Internet connectivity to areas not served by optical fiber, cable or other high speed terrestrial connections. However, using satellitelinks to supply high bandwidth has been difficult due to problems with inefficient performance of the Internet's TCP/IP protocol suite over satellite. We describe an architecture for improving the performance of TCP/IP protocols over heterogeneous network environments, especially networks containing satellite links. The end-to-end connection is split into segments, and the protocol on the satellite segment is optimized for the satellite link characteristics. TCP congestion control mechanisms are maintained on each segment, with some coupling between the segments to produce the effect of end-to-end TCP flow control. We have implemented this design and present results showing that using such gateways can improve throughput for individual connections by a large factor over paths containing a satellite link.The research and scientific content in this material has been published in the Proceedings of the SPIE, vol. 3528, February 1999, 169-180.</Center

Asynchronous Load Balancing and Auto-scaling: Mean-Field Limit and Optimal Design

We introduce a Markovian framework for load balancing where classical algorithms such as Power-of-$d$ are combined with asynchronous auto-scaling features. These allow the net service capacity to scale up or down in response to the current load within the same timescale of job dynamics. This is inspired by serverless frameworks such as Knative, used among others by Google Cloud Run, where servers are software functions that can be flexibly instantiated in milliseconds according to user-defined scaling rules. In this context, load balancing and auto-scaling are employed together to optimize both user-perceived delay performance and energy consumption. In the literature, these mechanisms are synchronous or rely on a central queue. The architectural novelty of our work is to consider an asynchronous and decentralized system, as in Knative, which takes scalability to the next level. Under a general assumption on the auto-scaling process, we prove a mean-field limit theorem that provides an accurate approximation for the system dynamics when the mean demand and nominal service capacity grow large in proportion. We characterize the fixed points of the mean-field limit model and provide a simple condition telling whether or not all the available servers need to be turned on to handle the incoming demand. Then, we investigate how to design optimal auto-scaling rules and find a general condition able to drive the mean-field dynamics to delay and relative energy optimality, a situation where the user-perceived delay and the relative energy wastage induced by idle servers vanish. The proposed optimality condition suggests to scale up capacity if and only if the mean demand exceeds the overall rate at which servers become idle and active. This yields the definition of tractable optimization frameworks to trade off between energy and performance, which we show as an application of our work