Robust bounds and throughput guarantees for closed multiclass queueing networks

Expressions are derived for the mean response times of each priority level in a multiserver M/M/m queue operating under preemptive resume scheduling. Exact results are obtained for cases where all priorities have the same mean service times; approximate results are obtained for the more general case where mean service times may differ. The results hold for any number of servers and any number of classes. For each priority level, it is assumed that arrivals are Poisson and service times are exponentially distributed.

A model for the service time structure in the single server queue is given embodying correlations between contiguous and near-contiguous service times. A number of results are derived in the case of Poisson arrivals both for equilibrium and the transient state. In particular, Kendall's (equilibrium) resultP(a departure leaves the queue empty) = 1 — (mean service time)/(mean inter-arrival time) is found still to hold good. The effect of the correlation on the mean and variance of the equilibrium queue length distribution is examined in a simple case.

We have conducted a research in order to clarify a movement of a top table tennis player using DLT method. We have tried to obtain basic data such as time intervals of various playing, times of shots, playing area, distance of movement and so on to plan a training program of a movement for table tennis.The objects of analysis were 5 games of YOO Nam Kyu, who was the SEOUL Olympic champion, in the 9th ASIAN Table Tennis Championships in Japan. The games were filmed at 60 frames/second with 6 VTR cameras which were installed at separate locations in the gymnasium. For the purpose of this analysis, the various time intervals are defined as follows: In-play Time was from the initial movement of the service to final contact with the ball during play. It is acknowledged that this definition differs slightly from the official ITTF regurations for “ball in play” time. Rally Time was from contact with the ball on service to final contact with the ball during play. Service Time was from the initial movement of the service to contact with the ball on service. Waiting Time was from one player's contact with the ball to the other player's contact.Two-dimensional coordinates on a TV monitor were computed with a VTR motion analyzer connected to a personal computer. These coordinates were then converted to real (X-Y-Z) coordinates using DLT method. The position of the player was estimated from the coordinates of the player's head (vertex), center of shoulders (acromions), center of hips (trochanterions) and center of ankles (malleolus fibulae points). Distance of movement and velocity of movement were computed for every body point in several directions; right to left and forward to backward (in relation to the table), and up to down. Distance of movement was a line that links the position of the player every 0.1 sec during Rally-time. Velocity of movement was calculated by dividing distance of movement by Rally-time for each rally.The results and findings are summarized as follows;1) Mean total In-play time was 144.63±27.69 sec (±SD). This represented about 20-30% of the games of which average was 611.75±33.50 sec long, meaning that about 70-80% of the games was excess time spent doing such things as picking up the ball or wiping off perspiration.2) Mean Service Time, Mean Rally Time, Mean In-play Time and Mean Waiting Time was 1.05±0.37 sec, 2.56±1.79 sec, 3.60±1.83 sec and 0.66±0.19 sec, respectively. This represented about 30% of In-play Time was Service Time and about 70% of it was Rally Time.3) Mean times of shots during 1 rally was 4.61±2.12. The distribution of times of shots during 1 rally showed that in the case of 74.6% of all rally, a player won or lost a point in 5 shots.4) The playing area for YOO was positioned at the side of his free hand in 4 games. In 1 game, it was positioned at the side of his racket hand. His main stroke of the game was different from previous 4 games.5) In each game, the distance of movement for YOO on a horizontal plane during Rally Time was between about 100m and 200m at the center of the ankles. And mean distance of movement for YOO on a horizontal plane during 1 rally was between about 3.5m and 4.0m at the center of the ankles. In the table tennis games, the player's repeated acceleration and deceleration in various directions was instantaneous.6) In each game, mean average velocity of movement for YOO on a horizontal plane during 1 rally was between 0.85m/sec and 1.08m/sec at the head, 0.90m/sec and 1.05m/sec at the center of the shoulders, 0.99m/sec and 1.18m/sec at the center of the hips and 1.36m/sec and 1.51m/sec at the center of the ankles.7) It seems that these new data and findings are very important to plan an efficient training program for table tennis coaches and players.

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.

short-paper Share on Tail asymptotics of the stationary distribution for a two-node generalized Jackson network Author: Masakiyo Miyazawa Tokyo University of Science, Noda, Chiba, Japan Tokyo University of Science, Noda, Chiba, JapanView Profile Authors Info & Claims ACM SIGMETRICS Performance Evaluation ReviewVolume 42Issue 2September 2014pp 70–72https://doi.org/10.1145/2667522.2667545Published:04 September 2014Publication History 1citation26DownloadsMetricsTotal Citations1Total Downloads26Last 12 Months0Last 6 weeks0 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

It is shown that among all work-conserving service disciplines that are independent of the future history, the first-come-first-served (FCFS) service discipline minimizes [maximizes] the average sojourn time in a G/GI/1 queueing system with new better [worse] than used in expectation (NBUE[NWUE]) service time distribution. We prove this result using a new basic identity of G/GI/1 queues that may be of independent interest. Using a relationship between the workload and the number of customers in the system with different lengths of attained service it is shown that the average sojourn time is minimized [maximized] by the least-attained-service time (LAST) service discipline when the service time has the decreasing [increasing] mean residual life (DMRL[IMRL]) property.

We consider a finite population $M/G/2$ queue in which the population size is M. We consider both the case of identical servers and also the situation when the two servers have different service time distributions. We assume that $M \gg 1$ and that the mean service times are small, specifically, $O(1/M )$. Then, we construct asymptotic expansions for the stationary distribution of the number of customers in the queueing system.

Scheduling is one of the most important factors used in scheduling processes insideCPU. CPU scheduling is a concept of multiprogramming, where the CPU is used to schedule the incoming processes alternately. Many algorithms can be used to schedule processesinside CPU, but not all can be real-time. Long waiting times and response times often be problems in scheduling processes in realtime. FIFO and Round Robin algorithms can be implemented to schedule the processes in realtime. In this paper, the authors schedule the process of several sensors that are used to collect landslide data. The data processing is sent by FIFO scheduling and Round Robin scheduling separately on the Internet of Things (IoT) device. The author only analyzes the performance of FIFO and Round Robin algorithms in scheduling the incoming processes in real-time on the IoT operating system by considering the waiting time and response time. The analysis is expected to create a quick response time and waiting time so that proper algorithm is decided to complement the IoT architecture in landslide detection. The FIFO and Round Robin algorithms are implementedat the Raspbian and Arch Linux operating systems in the IoT device, the Raspberry Pi 3 Model B, which uses a 64-bit 64-bit ARM Cortex-AS3 64-bit process at 1.2GHz.

We shall consider a many server (multiple channels in parallel) queueing process in which customers arrive at the queue according to a Poisson process. The service times are assumed to be independent and exponentially distributed. As usual, the service times are independent of the arrival process. We assume that no server is idle if there is a customer waiting, but that otherwise the service discipline is arbitrary. If there are n servers and we let Xn (t) denote the number of customers waiting or being served at time t, then it is well known that Xn (t) is a birth and death process with stationary transition probabilities. A very comprehensive analysis of this many server queue from the point of view of birth and death processes has been carried out by Karlin and McGregor [5].

Análisis del servicio de Urgencias aplicando teoría de líneas de espera

We consider a loss system with n channels and a finite or infinite overflow group, which is offered N different services, all having Poisson arrival processes. All calls have same bandwidth demand and mean service time, but the mean service time may be different on the primary group and the overflow group, corresponding to data traffic with different bandwidth allocation on primary (micro-cell = femto-cell) and overflow group (macro-cell = LTE-cell). Then using a result of Wallström we can calculate the Binomial moments of the total overflow traffic. Given a certain number of busy channels on the overflow group, we show by balance equations that the number of calls of each service will be Multinomial distributed with probabilities proportional with the arrival rates. Using a recent result of Newcomer & al, we then find moments (done up to fourth order) of individual overflow streams or any combinations of overflow streams. Thus we can find the correlation between services and for example the moments of some traffic streams which may overflow to one system, whereas other traffic streams may be blocked or overflow to another system.

Redundancy is an important strategy for reducing response time in multi-server distributed queueing systems. This strategy has been used in a variety of settings, but only recently have researchers begun analytical studies. The idea behind redundancy is that customers can greatly reduce response time by waiting in multiple queues at the same time, thereby experiencing the minimum time across queues. Redundancy has been shown to produce significant response time improvements in applications ranging from organ transplant waitlists to Google’s BigTable service. However, despite the growing body of theoretical and empirical work on the benefits of redundancy, there is little work addressing the questions of how many copies one needs to make to achieve a response time benefit, and the magnitude of the potential gains. In this paper we propose a theoretical model and dispatching policy to evaluate these questions. Our system consists of k servers, each with its own queue. We introduce the Redundancy-d policy, under which each incoming job makes copies at a constant number of servers, d, chosen at random. Under the assumption that a job’s service times are exponential and independent across servers, we derive the first exact expressions for mean response time in Redundancy-d systems with any finite number of servers, as well as expressions for the distribution of response time which are exact as the number of servers approaches infinity. Using our analysis, we show that mean response time decreases as d increases, and that the biggest marginal response time improvement comes from having each job wait in only d = 2 queues. The e-companion is available at https://doi.org/10.1287/opre.2016.1582 .

This paper presents a significant extension of the CSMA network access protocol. The protocol is based on the facts that, at high data rates, networks can contain multiple messages simultaneously over their span, and that in a ring, nodes needs only to detect the presence of a message arriving from the immediate up stream neighbor. When an incoming signal is detected, the node truncates the message it is presently sending instead of aborting it. The system has been named Carrier Sensed Multiple Access Ring Network, CSMA/RN.Analytical studies using three performance factors, wait or access time, service time and response or end-to-end travel time are presented. The service time is basically a function of the network rate; it changes by a factor of 4 between no load and full load. Wait time, which is zero for no load, remains small for load factors up to 70% of full load. Response time, which adds travel time while on the network to wait and service time, is mainly a function of network length, especially for longer distance networks.Simulation results are shown for CSMA/RN where messages are removed at the destination. Destination removal on an average increases network load capacity by a factor of 2, i.e., a 1 Gbps network can handle a 2 Gbps load. A wide range of local and metropolitan area network parameters including variations in message size, network length and node count are studied. In all cases performance is excellent, and message fracture usually remains less than a factor of 4. Throughput, even at overload conditions, remains high for the protocol. The nominal network rate is 1 Gbps; however, performance remains good for data rates as low as 200 Mbps. Finally, a scaling factor based upon the ratio of message to network length demonstrates that the results of this paper, and hence, the CSMA/RN protocol, are applicable to wide area networks.

We consider a queue where the server is the Euclidean space, and the customers are random closed sets (RACSs) of the Euclidean space. These RACSs arrive according to a Poisson rain and each of them has a random service time (in the case of hail falling on the Euclidean plane, this is the height of the hailstone, whereas the RACS is its footprint). The Euclidean space serves customers at speed 1. The service discipline is a hard exclusion rule: no two intersecting RACSs can be served simultaneously and service is in the first-in–first-out order, i.e. only the hailstones in contact with the ground melt at speed 1, whereas the others are queued. A tagged RACS waits until all RACSs that arrived before it and intersecting it have fully melted before starting its own melting. We give the evolution equations for this queue. We prove that it is stable for a sufficiently small arrival intensity, provided that the typical diameter of the RACS and the typical service time have finite exponential moments. We also discuss the percolation properties of the stationary regime of the RACS in the queue.

Using sample path analysis we show that under the same load the mean delay in queue in the M/G/2 system is smaller than that in the corresponding M/G/1 system, when the service time has either the DMRL or NBU property and the service discipline is FCFS. The proof technique uses a new device that equalizes the work in a two server system with that in a single sterver system. Other interesting quantities such as the average difference in work between the two servers in the GI/G/2 system and an exact alternate derivation of the mean delay in the M/M/2 system from sample path analysis are presented. For the same load, we also show that the mean delay in the M/G/C system with general service time distribution is smaller than that in the M/G/1 system when the traffic intensity is less than 1/c.