Infinite Buffer Capacity Research Articles

Pricing in vehicle sharing systems: optimization in queuing networks with product forms

One-way vehicle sharing systems (VSS) such as Vélib’ Paris are flourishing. The usefulness of VSS for users is highly impacted by the availability of vehicles and parking spots. Most existing systems are ruled by the trips of users. We study the potential interest of influencing the users to improve the performance of the system. We assume that each user is associated with a pair origin–destination (O–D) of stations, and only interacts with the system if his O–D trip is available. We consider leverage that can influence the rate of user requests for each pair O–D, such as a price that will be prohibitive for a prescribed proportion of users. We focus on optimizing the number of trips taken in the system. To provide exact formulas and analytical insights, transportation times are assumed to be null, stations to have infinite capacities and the demand to be stationary over time. In other words, VSS are modelled as closed queuing networks with infinite buffer capacity and Markovian demands. We propose a heuristic based on computing a Maximum Circulation on the demand graph together with a convex integer program solved optimally by a greedy algorithm. For M stations and N vehicles, the performance ratio of this heuristic is proved to be exactly N/(N+M-1). We discuss our understanding on the possibility of extending this result to more realistic models in the perspectives. The complexity of computing optimum policies remains open. Insights on this issue are provided in the Appendix. The Appendix also contains an example showing that VSS can have poor performances without regulation.

Exact Tail Asymptotics of a Tandem Queue with LRD Service Times

In this work we compute the exact tail asymptotics of the stationary sojourn time Z, associated to the discretetime tandem queue D/G/1/∞ → ∙/G/1/∞, with constant release rate, infinite buffer capacity, and with service time sequences generated by the busy server processes of the two M 1/G 1/∞ and M 2/G 2/∞independent queues exhibiting long-range dependence. We choose the same regularly varying distribution with parameter α > 1 for the general distributions G 1 and G 2. We show that the exact asymptotics of the sojourn time is a specific regularly varying function under some assumptions on the parameters.

Exact Tail Asymptotics of a Queue with LRD Input Traffic

In this work we compute the exact tail asymptotics of the stationary workload W, associated to a discretetime single server queue, with constant release rate, infinite buffer capacity, and with M/G/∞ input traffic exhibiting long-range dependence. We choose a regularly varying distribution with parameter α > 1 for the general distribution G. We show that the exact asymptotics of the workload is a specific regularly varying function under some assumptions on the parameters.

APPROXIMATE MODEL FOR A MERGE CONFIGURATION OF MULTISERVERS WITH FINITE CAPACITY INTERMEDIATE BUFFERS

We consider a queueing network consisting of multiservers in par- allel and connected to a merger queue. All servers have an infinite capacity buffers. The configuration is decomposed into two subsystems: merging multi- servers and merger server and then analyzed in isolation. All times are assumed to be exponentially distributed. First we set and solve the equations for the ag- gregated merger queue, then express the occupancy probabilities of the original queue through the probabilities of the aggregated one, which reduces signifi- cantly the number of equations describing the behavior of the network. Using the fore-mentioned result, we derive expressions for the occupancy probabilities and other parameters of the merging queue.

An Optimal Algorithm for a Special Flow Shop Problem with Infinite Buffer Capacity

In this paper, a two-machine flow shop problem with infinite buffer capacity is considered. Each of jobs is identical and has two tasks. The first task can be processed on either machine, called flexible task, while the second task must be processed on the second machine and can't be processed unless the first task has been processed. There is infinite buffer capacity between two machines. The problem is to determine the assignment of the flexible tasks to the machines for each job, with the objective of maximizing the makespan. We present an optimal algorithm for this problem.

Solving Scheduling Problems in Distribution Centers by Mixed Integer Linear Programming Formulations

AbstractThis paper considers the problem of scheduling the internal operations of a distribution center: a system to which goods arrive from several suppliers and are forwarded to several customers. Internal operations consist essentially in unloading incoming cases and loading outgoing ones. Thus, the internal operations are divided in three phases: de-consolidation, sorting and consolidation. The objective is to minimize the total operation time determining the optimal sequence of the operations in the three phases.Starting from a previous formulation, we propose two new Mixed Integer Linear Programming models assuming infinite buffer capacities, in order to deal with instances of larger size. Some preliminary results show promising prospectives for the effectiveness of the new approaches.

Random-Access Poisson Networks: Stability and Delay

We consider a Poisson network of sources, each with a destination at a given distance and a buffer of infinite capacity. Assuming independent Bernoulli arrivals, we characterize the stability region when one or two classes of users are present in the network. We then derive a fixed-point equation that determines the success probability of the typical source-destination link and evaluate the mean delay at each buffer.

A fluid queue modulated by two independent birth–death processes

We present a fluid queue model driven by two independent finite state birth–death processes with the objective to study the buffer occupancy distribution in any intermediate node in a communication network. In a communication network, at any node, the arrival and service of the packets are with variable rates. To model this scenario we develop a fluid queue with an infinite capacity buffer which receives fluid at variable rate and also releases fluid at variable rates. Because of variable inflow and outflow rates of the fluid, the proposed fluid queue is driven by the current states of two independent finite state birth–death processes evolving in the background which on merging give rise to a continuous time Markov chain which is not a birth–death process. Using the fluid queue model, we obtain the steady-state distribution of the buffer occupancy at any intermediate node during packet transmission in a communication network. As a special case, we consider a wireless network based on the IEEE 802.11 standard. We present the buffer occupancy distribution at any intermediate node in closed form with a numerical illustration. Along with buffer occupancy distribution, we also obtain various performance measures such as expected buffer content, average throughput, server utilization and mean delay which are relevant to packet transmission in such a communication network. Finally, we present numerical results to illustrate the feasibility of the proposed model. The results are in accordance with the expected behavior of these performance measures.

PEMODELAN ALJABAR MAX-PLUS DAN EVALUASI KINERJA JARINGAN ANTRIAN FORK-JOIN TAKSIKLIK DENGAN KAPASITAS PENYANGGA TAKHINGGA

This paper aims to model and determine the service cycle completion time of noncyclic fork-join queueing networks with infinite buffer capacity, using max-plus algebra. The finding show that the dynamics of the noncyclic fork-join queuing networks with infinite buffer capacity can be modeled into a matrix equation over max-plus algebra. We can also show that the service cycle completion time of queuing networks is a max-plus eigenvalues of the matrix in the equation.slklsklslsllsllllllllllllllllllllll

Exponential queuing system with negative customers and bunker for ousted customers

Consideration was given to the queuing system with Poisson flows of incoming positive and negative customers. For the positive customers, there is an infinite-capacity buffer. The arriving negative customer knocks out a positive customer queued in the buffer and moves it to an infinite-capacity buffer of ousted customers (bunker). If the buffer is empty, then the negative customer discharges the system without affecting it. After servicing the current customer, the server receives a customer from the buffer or, if the buffer is empty, the bunker. The customers arriving from both the buffer and bunker are distributed exponentially with the same parameter. Relations for calculation of the stationary distributions of the queues in the buffer and bunker were obtained.

Production Control and Steady-State Performance Analysis for A Two-stage Manufacturing System with Finite Buffer Sizes

A two-station tandem manufacturing system with limited buffer sizes and production capacity is considered. The problem is to examine the stability of the system and to control the service rates to meet an exogenous Poisson demand. A sufficient and necessary condition for the system stability is provided. It is shown that the optimal control policy for this finite buffer capacity problem has the similar structural properties to that of the infinite buffer capacity problem. Three threshold-type control policies are presented and their stability conditions are shown to be the same. The stationary distributions under two threshold policies are obtained, which can then be used to compute steady-state performance measures and find the optimal threshold values. Numerical examples are given to demonstrate the results.

A game-theoretic analysis of denial of service attacks in wireless random access

In wireless access, transmitter nodes need to make individual decisions for distributed operation and do not necessarily cooperate with each other. We consider a single-receiver random access system of non-cooperative transmitters with the individual objectives of optimizing their throughput rewards, transmission energy costs and delay costs. The non-cooperative transmitter behavior may be purely selfish or may also reflect malicious objectives of generating interference to prevent the successful transmissions of the other nodes as a form of denial of service attack. Our goal is to evaluate the interactions between selfish and malicious nodes that have the dual objectives of optimizing their individual performance measures and blocking the packet transmissions of the other selfish nodes. We assume saturated packet queues of infinite buffer capacities and consider a general multi-packet reception channel that allows packet captures in the presence of simultaneous transmissions. In this context, we formulate a non-cooperative random access game of selecting the individual probabilities of transmitting packets to a common receiver. We derive the non-cooperative transmission strategies in Nash equilibrium. The analysis provides insights for the optimal strategies to block random access of selfish nodes as well as the optimal defense mechanisms against the possible denial of service attacks of malicious nodes in wireless networks. The results are also compared with the cooperative equilibrium strategies that optimize the total system utility (separately under random access and scheduled access). A pricing scheme is presented to improve the non-cooperative operation. For distributed implementation, we formulate a repeated game of the best-response strategy updates and introduce adaptive heuristics (based on the channel feedback only) provided that the system parameters are not explicitly known at the individual transmitters.

Multiclass Markovian fluid queues

This paper considers a multiclass Markovian fluid queue with a buffer of infinite capacity. Input rates of fluid flows in respective classes and the drain rate from the buffer are modulated by a continuous-time Markov chain with finite states. We derive the joint Laplace-Stieltjes transform for the stationary buffer contents in respective classes, assuming the FIFO service discipline. Further we develop a numerically feasible procedure to compute the joint and marginal moments of the stationary buffer contents in respective classes. Some numerical examples are then provided.

Output analysis of multiclass fluid models with static priorities

We consider a stochastic fluid flow model with a single server and K infinite capacity buffers. The input to the k -th buffer is a Markovian on-off process that transmits fluid at a constant rate p k while it is on and at rate 0 while it is off. The fluid is emptied from the buffers by a single server at a constant rate μ according to a static priority service discipline in which class 1 fluid has the highest and class K fluid has the lowest priority. The output process of class k is defined to be on if fluid of class k is leaving the buffer at a positive rate and off otherwise. In this paper we derive an exact method for computing the mean on-time and the mean off-time of the output process of class k . We illustrate the method with a numerical example.

Investigation of batch data flow transmission parameters

Rapid growth and increasing requirements for service quality, reliability, and efficiency have made traffic evaluation an essential consideration in design and operation of data transmission networks. In this paper we analyse performance measures of data transmission network servicing batch data flows. The article provides analysis of the one channel queuing system transmitting data packet flow general distributed. In this article we introduce queuing system with finite and infinite buffer capacity. In this article we analyse such data packets transmission performance param- eters: average time spent by data packet in system, data packet delay variation, data packet loss. The data packet arrival rate and channel data packet transmission rate are independent of system state. A key mechanism of the proposed traffic model is that packet time spent in the system depends on channel utilization level, packet flow type and size of transmit- ted data. The proposed simulation model can be used when packet interarrival time follows such distributions: Pareto, Poisson, uniform, normal distribution. Simulation results of performance measures are defined by mathematical mod- els. Considering simulation results recommendations were proposed to improve performance measures for batch data flow transmission over data networks.

INVESTIGATION OF BATCH DATA FLOW TRANSMISSION PARAMETERS

Rapid growth and increasing requirements for service quality, reliability, and efficiency have made traffic evaluation an essential consideration in design and operation of data transmission networks. In this paper we analyse performance measures of data transmission network servicing batch data flows. The article provides analysis of the one channel queuing system transmitting data packet flow general distributed. In this article we introduce queuing system with finite and infinite buffer capacity. In this article we analyse such data packets transmission performance parameters: average time spent by data packet in system, data packet delay variation, data packet loss. The data packet arrival rate and channel data packet transmission rate are independent of system state. A key mechanism of the proposed traffic model is that packet time spent in the system depends on channel utilization level, packet flow type and size of transmitted data. The proposed simulation model can be used when packet interarrival time follows such distributions: Pareto, Poisson, uniform, normal distribution. Simulation results of performance measures are defined by mathematical models. Considering simulation results recommendations were proposed to improve performance measures for batch data flow transmission over data networks.

Divisible load scheduling in distributed system with buffer constraints: genetic algorithm and linear programming approach

Scheduling divisible loads in a single-level tree network/system with processors having finite buffer size is addressed. In earlier studies in divisible load scheduling the processors are assumed to have no buffer constraints or have infinite buffer capacity. Hence, the processing time and the load fractions assigned to the processors in the network are obtained by assuming that all the processors will stop computing at the same instant in time. Also in earlier studies, a closed-form expression for the processing time is derived, and using this closed-form expression, an optimal sequence of load distribution is obtained. When the processors in the network have finite buffer then this assumption that all the processors stop computing at the same time instant is not valid. So for a network with buffer constraints, there are two important problems: (i) for a given sequence of load distribution, how to obtain the processing time, and the load fractions assigned to the processors, and (ii) for a given network, how to obtain the optimal sequence of load distribution. Here problem (i) of obtaining the processing time and the load fractions assigned to the processors in the network, for a given sequence of load distribution, is not difficult to solve and is modelled as a linear programming problem and its solution is obtained. For a single-level tree network with m child processors there are m! sequences of load distribution. The optimal sequence of load distribution is the sequence of load distribution, for which the processing time of the entire processing load is a minimum. So, problem (ii) of obtaining the optimal sequence of load distribution is difficult. It is shown in an earlier study that this problem (ii) is NP-Hard. In this paper, genetic algorithm (GA) is used for problem (ii) to obtain the sequence of load distribution. Various issues related to genetic algorithms such as solution representation, selection methods and genetic operators are presented. Numerical results are provided to show the advantages of GA methodology.

The [formula omitted] G-queue with heterogeneous servers: Steady state solution and an application to performance evaluation

A new queue, referred to here as the HetSigma queue, in the Markovian framework, is proposed in order to model nodes in modern telecommunication networks. The queue has many of the necessary ingredients, such as joint (or individual) Markov modulation of the arrival and service processes, superposition of K CPP (compound Poisson process) streams of (positive) customer arrivals, and a CPP of negative customer arrival stream in each of the modulating phases, a multiserver with c non-identical (can also be identical) servers, GE (generalised exponential) service times in each of the modulating phases and a buffer of finite or infinite capacity. Thus, the model can accommodate correlations of the inter-arrival times (of batches), and geometric as well as non-geometric batch size distributions of customers in both arrivals and services. The use of negative customers can facilitate modelling server failures, packet losses, load balancing, channel impairment in wireless networks, and in many other applications. An exact and computationally efficient solution of this new queue for steady state probabilities and performance measures is developed and presented. A non-trivial application of the new queue to the performance evaluation of a wireless communication system is presented, along with numerical results, to illustrate the efficacy of the proposed method. The use of negative customers is also demonstrated. The new queue, perhaps with further evolution, has the potential to emerge as a generalised Markovian node model.

Two-moment approximations for analysing a series of automated workstations

In this research we develop two-moment approximation equations for the analysis of a series of automated workstations with infinite buffer capacity. An automated workstation is a server with deterministic processing times that experiences random operating times between failures, and then subsequent random repair times. The distribution of job inter-departure times from a workstation receiving input from an automated workstation is derived. From this distribution, expressions for the mean and variance of job inter-departure times from a workstation are obtained. These are then used as a basis for ‘linking’ workstations in a two-workstation aggregation approach. This method is compared to modelling such a system as a series of G/G/1 queues. The analysis method is easily implemented in a spreadsheet. Extensive computational experiments demonstrate the effectiveness of the overall approach.

FLUID MODELS WITH JUMPS

ABSTRACT In this paper we study a general stochastic fluid model with a single infinite capacity buffer, where the buffer content can change continuously as well as by instantaneous upward jumps. The continuous as well as the instantaneous change is modulated by an external environment process modelled as a finite state continuous time Markov chain. The Laplace-Stieltjes transform of the steady-state joint distribution of the buffer content and the state of the environment is determined explicitly in terms of the solutions of a generalized eigenvalue problem. The methodology is illustrated by several well-known queueing problems.