First-come First-served Service Research Articles

Scheduling the Real-Time Transmission of Periodic Measurements in 802.15.4 Wireless Sensor Network

Wireless sensor networks (WSN) are a major technological innovation developed in recent years with many important applications, for example in Cyber-Physical Systems and Internet of Things environments. Although there are many proposals for handling real-time traffic in WSNs, most of them fall into best-effort mechanisms that do not provide real-time guarantees. At the MAC level, the IEEE 802.15.4 standard defines a reservation mechanism called Guaranteed Time Slots (GTS) that uses a first-come first-served service policy, which is not enough to ensure the real-time delivery of packets. In this work, we present a formal definition of the scheduling problem for a sensor network using a reservation mechanism (such as GTS) that provides guarantees for the real-time delivery of packets. We also present a heuristic approach for finding feasible schedules when possible or determining if the requirements of a set of sensors are not feasible.

Output analysis of a single-buffer multiclass queue: FCFS service

We consider an infinite capacity buffer where the incoming fluid traffic belongs to K different types modulated by K independent Markovian on-off processes. The kth input process is described by three parameters: (λk, μk, rk), where 1/λk is the mean off time, 1/μk is the mean on time, and rk is the constant peak rate during the on time. The buffer empties the fluid at rate c according to a first come first served (FCFS) discipline. The output process of type k fluid is neither Markovian, nor on-off. We approximate it by an on-off process by defining the process to be off if no fluid of type k is leaving the buffer, and on otherwise. We compute the mean on time τkon and mean off time τkoff. We approximate the peak output rate by a constant rko so as to conserve the fluid. We approximate the output process by the three parameters (λko, μko, rko), where λko = 1/τkoff, and μko = 1/τkon. In this paper we derive methods of computing τkon, τkoff and rko for k = 1, 2,…, K. They are based on the results for the computation of expected reward in a fluid queueing system during a first passage time. We illustrate the methodology by a numerical example. In the last section we conduct a similar output analysis for a standard M/G/1 queue with K types of customers arriving according to independent Poisson processes and requiring independent generally distributed service times, and following a FCFS service discipline. For this case we are able to get analytical results.

Output analysis of a single-buffer multiclass queue: FCFS service

We consider an infinite capacity buffer where the incoming fluid traffic belongs to K different types modulated by K independent Markovian on-off processes. The kth input process is described by three parameters: (λ k , μ k , r k ), where 1/λ k is the mean off time, 1/μ k is the mean on time, and r k is the constant peak rate during the on time. The buffer empties the fluid at rate c according to a first come first served (FCFS) discipline. The output process of type k fluid is neither Markovian, nor on-off. We approximate it by an on-off process by defining the process to be off if no fluid of type k is leaving the buffer, and on otherwise. We compute the mean on time τ k on and mean off time τ k off. We approximate the peak output rate by a constant r k o so as to conserve the fluid. We approximate the output process by the three parameters (λ k o, μ k o, r k o), where λ k o = 1/τ k off, and μ k o = 1/τ k on. In this paper we derive methods of computing τ k on, τ k off and r k o for k = 1, 2,…, K. They are based on the results for the computation of expected reward in a fluid queueing system during a first passage time. We illustrate the methodology by a numerical example. In the last section we conduct a similar output analysis for a standard M/G/1 queue with K types of customers arriving according to independent Poisson processes and requiring independent generally distributed service times, and following a FCFS service discipline. For this case we are able to get analytical results.

An overview of Brownian and non-Brownian FCLTs for the single-server queue

We review functional central limit theorems (FCLTs) for the queue-content process in a single-server queue with finite waiting room and the first-come first-served service discipline. We emphasize alternatives to the familiar heavy-traffic FCLTs with reflected Brownian motion (RBM) limit process that arise with heavy-tailed probability distributions and strong dependence. Just as for the familiar convergence to RBM, the alternative FCLTs are obtained by applying the continuous mapping theorem with the reflection map to previously established FCLTs for partial sums. We consider a discrete-time model and first assume that the cumulative net-input process has stationary and independent increments, with jumps up allowed to have infinite variance or even infinite mean. For essentially a single model, the queue must be in heavy traffic and the limit is a reflected stable process, whose steady-state distribution can be calculated by numerically inverting its Laplace transform. For a sequence of models, the queue need not be in heavy traffic, and the limit can be a general reflected Levy process. When the Levy process representing the net input has no negative jumps, the steady-state distribution of the reflected Levy process again can be calculated by numerically inverting its Laplace transform. We also establish FCLTs for the queue-content process when the input process is a superposition of many independent component arrival processes, each of which may exhibit complex dependence. Then the limiting input process is a Gaussian process. When the limiting net-input process is also a Gaussian process and there is unlimited waiting room, the steady-state distribution of the limiting reflected Gaussian process can be conveniently approximated.

Predicting Queueing Delays

This paper investigates the possibility of predicting each customer's waiting time in queue before starting service in a multiserver service system with the first-come first-served service discipli...

Predicting Queueing Delays

This paper investigates the possibility of predicting each customer's waiting time in queue before starting service in a multiserver service system with the first-come first-served service discipline, such as a telephone call center. A predicted waiting-time distribution or an appropriate summary statistic such as the mean or the 90th percentile may be communicated to the customer upon arrival and possibly thereafter in order to improve customer satisfaction. The predicted waiting-time distribution may also be used by the service provider to better manage the service system, e.g., to help decide when to add additional service agents. The possibility of making reliable predictions is enhanced by exploiting information about system state, including the number of customers in the system ahead of the current customer. Additional information beyond the number of customers in the system may be obtained by classifying customers and the service agents to which they are assigned. For nonexponential service times, the elapsed service times of customers in service can often be used to advantage to compute conditional-remaining-service-time distributions. Approximations are proposed to convert the distributions of remaining service times into the distribution of the desired customer waiting time. The analysis reveals the advantage from exploiting additional information.

A conservation law for single-server queues and its applications

We establish a conservation law for G/G/1 queues with any work-conserving service discipline using the equilibrium equations, also called the basic equations. We use this conservation law to prove an extremal property of the first-come firstserved (FCFS) service discipline: among all service disciplines that are work-conserving and independent of remaining service requirements for individual customers, the FCFS service discipline minimizes [maximizes] the mean sojourn time in a G/G/1 queue with independent (but not necessarily identical) service times with a common mean and new better [worse] than used (NBUE[NWUE]) distributions. This extends recent results of Halfin and Whitt (1990), Righter et al. (1990) and Yamazaki and Sakasegawa (1987a,b). In addition we use the conservation law to obtain an approximation for the mean queue length in a GI/GI/1 queue under the processor-sharing service discipline with finite degree of multiplicity, called LiPS discipline. Several numerical examples are presented which support the practical usefulness of the proposed approximation.

A conservation law for single-server queues and its applications

We establish a conservation law forG/G/1 queues with any work-conserving service discipline using the equilibrium equations, also called the basic equations. We use this conservation law to prove an extremal property of the first-come firstserved (FCFS) service discipline: among all service disciplines that are work-conserving and independent of remaining service requirements for individual customers, the FCFS service discipline minimizes [maximizes] the mean sojourn time in aG/G/1 queue with independent (but not necessarily identical) service times with a common mean and new better [worse] than used (NBUE[NWUE]) distributions. This extends recent results of Halfin and Whitt (1990), Righter et al. (1990) and Yamazaki and Sakasegawa (1987a,b). In addition we use the conservation law to obtain an approximation for the mean queue length in aGI/GI/1 queue under the processor-sharing service discipline with finite degree of multiplicity, called LiPS discipline. Several numerical examples are presented which support the practical usefulness of the proposed approximation.

Path delays in communication networks

A communication network is modelled by a weighted graph. The vertices of the graph represent stations with storage capabilities, while the edges of the graph represent communication channels (or other information processing media). Channel capacity weights are assigned to the edges of the network. The network is assumed to operate in a store-and-forward manner, so that when a channel is busy the messages directed into it are stored at the station, joining there a queue which is governed by a first-come first-served service discipline.

Communication networks: Message path delays

A communication network is modeled by a weighted graph. The vertices of the graph represent stations with storage capabilities, while the edges of the graph represent communication channels (or other information processing media). Channel capacity weights are assigned to the edges of the network. The network is assumed to operate in a store-and-forward manner, so that when a channel is busy the messages directed into it are stored at the station, where it joins a queue that is governed by a first-come first-served service discipline. Assuming that fixed-length messages arrive at random at the network, following the statistics of a Poisson point process, we solve for the steady-state distributions of the message overall delay time, for the average message waiting times at the individual stations, for the average memory size requirements at the stations, as well as for other statistical characteristics of the message flow along a communication path.