First-in First-out Discipline Research Articles

Covert Cycle Stealing in a Single FIFO Server

Consider a setting where Willie generates a Poisson stream of jobs and routes them to a single server that follows the first-in first-out discipline. Suppose there is an adversary Alice, who desires to receive service without being detected. We ask the question: What is the number of jobs that she can receive covertly, i.e., without being detected by Willie? In the case where both Willie and Alice jobs have exponential service times with respective rates μ 1 and μ 2 , we demonstrate a phase-transition when Alice adopts the strategy of inserting a single job probabilistically when the server idles: over n busy periods, she can achieve a covert throughput, measured by the expected number of jobs covertly inserted, of O (√ n ) when μ 1 < 2 μ 2 , O (√ n log n ) when μ 1 = 2μ 2 , and O ( n μ 2 /μ 1 ) when μ 1 > 2μ 2 . When both Willie and Alice jobs have general service times, we establish an upper bound for the number of jobs Alice can execute covertly. This bound is related to the Fisher information. More general insertion policies are also discussed.

Моделирование компьютерных систем с FIFO-дисциплиной обработки прерываний

Дисциплина FIFO (First In First Out) обработки прерываний достаточно широко используется в ЭВМ Фон Неймановского типа, применяемых в информационных и цифровых управляющих системах. Цель реализации подобного режима работы — оптимизация времени доступа к данным — достижима только при наличии адекватной модели, описывающей систему. Аналитическая модель построена с использованием фундаментального математического аппарата сетей Петри-Маркова. Первичная Петри-Марковская модель разделена на иерархические уровни, соответствующие количеству заявок на обработку прерываний в очереди. Показано, что с текущего уровня возможно переключение, как на предыдущий, так и на последующий уровни прерываний. Получены зависимости для определения времени пребывания на текущем уровне и вероятностей переключения на сопряженные уровни. Предложен метод преобразования Петри-Марковской модели в полумарковский процесс. Показано, что структура подобного полумарковского процесса представляет собой бинарное дерево. Получены зависимости для определения временных и вероятностных характеристик блужданий по бинарному дереву.

FIFO Time Petri Nets for conflicts handling

This paper considers time Petri nets (TPN for short) and its classical semantics (Merlin's semantics). It discusses an alternative semantics, called FIFO-semantics. FIFO-semantics is based on ages of tokens and manages tokens w.r.t. FIFO (First In First Out) discipline (FIFO-TPN). This paper first shows that FIFO-TPN are very appropriate to deal with some conflicting situations (which cannot always be modelled by the classical semantics) and shows its conciseness for conflicts modeling. Then, it compares the theoretical expressiveness of FIFO-TPN vs classical-TPN and shows that, despite FIFO-TPN add expressiveness in the general case, for bounded models, they have the same expressive power w.r.t. weak timed bisimulation.

Geographical variations in the benefit of applying a prioritization system for cataract surgery in different regions of Spain.

BackgroundIn Spain, there are substantial variations in the utilization of health resources among regions. Because the need for surgery differs in patients with appropriate surgical indication, introducing a prioritization system might be beneficial. Our objective was to assess geographical variations in the impact of applying a prioritization system in patients on the waiting list for cataract surgery in different regions of Spain by using a discrete-event simulation model.MethodsA discrete-event simulation model to evaluate demand and waiting time for cataract surgery was constructed. The model was reproduced and validated in five regions of Spain and was fed administrative data (population census, surgery rates, waiting list information) and data from research studies (incidence of cataract). The benefit of introducing a prioritization system was contrasted with the usual first-in, first-out (FIFO) discipline. The prioritization system included clinical, functional and social criteria. Priority scores ranged between 0 and 100, with greater values indicating higher priority. The measure of results was the waiting time weighted by the priority score of each patient who had passed through the waiting list. Benefit was calculated as the difference in time weighted by priority score between operating according to waiting time or to priority.ResultsThe mean waiting time for patients undergoing surgery according to the FIFO discipline varied from 1.97 months (95% CI 1.85; 2.09) in the Basque Country to 10.02 months (95% CI 9.91; 10.12) in the Canary Islands. When the prioritization system was applied, the mean waiting time was reduced to a minimum of 0.73 months weighted by priority score (95% CI 0.68; 0.78) in the Basque Country and a maximum of 5.63 months (95% CI 5.57; 5.69) in the Canary Islands. The waiting time weighted by priority score saved by the prioritization system varied from 1.12 months (95% CI 1.07; 1.16) in Andalusia to 2.73 months (95% CI 2.67; 2.80) in Aragon.ConclusionThe prioritization system reduced the impact of the variations found among the regions studied, thus improving equity. Prioritization allocates the available resources within each region more efficiently and reduces the waiting time of patients with greater need. Prioritization was more beneficial than allocating surgery by waiting time alone.

Queues, stores, and tableaux

Consider the single-server queue with an infinite buffer and a first-in–first-out discipline, either of type M/M/1 or Geom/Geom/1. Denote by 𝒜 the arrival process and by s the services. Assume the stability condition to be satisfied. Denote by 𝒟 the departure process in equilibrium and by r the time spent by the customers at the very back of the queue. We prove that (𝒟, r) has the same law as (𝒜, s), which is an extension of the classical Burke theorem. In fact, r can be viewed as the sequence of departures from a dual storage model. This duality between the two models also appears when studying the transient behaviour of a tandem by means of the Robinson–Schensted–Knuth algorithm: the first and last rows of the resulting semistandard Young tableau are respectively the last instant of departure from the queue and the total number of departures from the store.

Queues, stores, and tableaux

Consider the single-server queue with an infinite buffer and a first-in–first-out discipline, either of type M/M/1 or Geom/Geom/1. Denote by 𝒜 the arrival process and by s the services. Assume the stability condition to be satisfied. Denote by 𝒟 the departure process in equilibrium and by r the time spent by the customers at the very back of the queue. We prove that (𝒟, r) has the same law as (𝒜, s), which is an extension of the classical Burke theorem. In fact, r can be viewed as the sequence of departures from a dual storage model. This duality between the two models also appears when studying the transient behaviour of a tandem by means of the Robinson–Schensted–Knuth algorithm: the first and last rows of the resulting semistandard Young tableau are respectively the last instant of departure from the queue and the total number of departures from the store.

A Strategic Model for Dynamic Traffic Assignment

In this paper, we propose a model of dynamic traffic assignment where strategic choices are an integral part of user behaviour. The model is based on a discrete-time description of flow variation through a road network involving arcs with rigid capacities. In such network, a driver's strategy consists in a rule that assigns to each node of the network a set of arcs in the forward star of that node, sorted according to some preference order. The main element of the model is a ‘within-day’ submodel where strategic volumes are loaded onto the network in accordance with the first-in first-out discipline and user preferences. An equilibrium assignment is achieved when expected delays of active strategies are minimal, for every origin-destination pair. We prove the existence of such an assignment and provide numerical results on test networks.

Extending the effective bandwidth concept to networks with priority classes

ATM switches are now being designed to allow connections to be partitioned into priority classes, with packets being emitted for higher priority classes before packets are emitted for lower priority classes. Accordingly, allocation of network resources based on different priority levels is becoming a realistic possibility. Thus, we need new methods for connection admission control and capacity planning that take account of the priority structure. We show that the notion of effective bandwidths can be used for these purposes when appropriately extended. The key is to have admissibility of a set of connections determined by a linear constraint for each priority level, involving a performance criterion for each priority level. For this purpose, connections are assigned more than one effective bandwidth, one for its own priority level and one for each lower priority level. Candidate effective bandwidths for each priority level can be determined by using previous methods associated with the first-in first-out discipline. The proposed effective bandwidth structure makes it possible to apply product-form stochastic loss network models to perform dimensioning.

On the cutoff fraction distribution for TASI systems with FIFO discipline

This paper deals with time-assigned speech interpolation (TASI) systems. We show that under the assumptions of an exponential distribution for both talkspurt and silence duration, and the first-in first-out (FIFO) discipline, the percentage of talkspurts totally cut off coincides with the well-known formula of Weinstein (1978). In addition, we provide the probability distribution function (PDF) of the portion that a talkspurt is cut off under the FIFO discipline.

Using Distributed-Event Parallel Simulation to Study Departures from Many Queues in Series

In this paper we describe an application of distributed-event parallel simulation to study the transient behavior of a large non-Markovian network of queues. In particular, we implemented the parallel-prefix-based algorithm of Greenberg, Lubachevsky, and Mitrani [13,14] on the 8,192-processor CM-2 Connection machine and the 16,384-processor MasPar computer to simulate the departure times D(k, n) of the kth customer from the nth queue in a long series of single-server queues. Each queue has unlimited waiting space and uses the first-in first-out discipline. The service times of all the customers at all the queues are i.i.d. with a general distribution, and the system starts out with k customers in the first queue and all other queues empty. Glynn and Whitt [11] established limit theorems for this model, but very little could be said about the limits themselves. The simulation results presented here describe the limits and the quality of the approximations resulting from using the limits for finite k and n. Indeed, the simulations suggest interesting conjectures. For this model speeding up a single long run is far superior to independent replications, because very long runs are required to obtain unbiased estimates of the desired quantities and the variance of the estimator at the end of the run is small. The achieved simulation rate was about 17 billion service completions per hour, which is a speedup by about a factor of 100 compared to simulation on a conventional single-processor machine. This speedup contributed greatly to performing the desired experiments.

Deterministic model and transient analysis of virtual circuits

A model for a virtual circuit in the form of a tandem of servers that process incoming packets using a FIFO (first-in, first-out) discipline is proposed. The service times are assumed to be known completely. These may differ from packet to packet and from server to server. The model permits a variety of buffer or transit time constraints to be incorporated into the model. Several results that help one to understand the transient behavior of a virtual circuit are presented. On the basis of these results, a number of schemes that may be used to determine the time when the next packet must be sent over the network are presented. Transit delay and throughput are used to evaluate a given schedule. Solutions are given for maximum throughput, minimum transit delay, and maximum throughput under transit delay constraints. It is expected that these results will have a substantial bearing on the study of congestion control policies in computer networks, particularly those based on predicting network behavior. >

Queues with service times and interarrival times depending linearly and randomly upon waiting times

We consider a modification of the standardG/G/1 queue with unlimited waiting space and the first-in first-out discipline in which the service times and interarrival times depend linearly and randomly on the waiting times. In this model the waiting times satisfy a modified version of the classical Lindley recursion. We determine when the waiting-time distributions converge to a proper limit and we develop approximations for this steady-state limit, primarily by applying previous results of Vervaat [21] and Brandt [4] for the unrestricted recursionYn+1=CnYn+Xn. Particularly appealing for applications is a normal approximation for the stationary waiting time distribution in the case when the queue only rarely becomes empty. We also consider the problem of scheduling successive interarrival times at arrival epochs, with the objective of achieving nearly maximal throughput with nearly bounded waiting times, while making the interarrival time sequence relatively smooth. We identify policies depending linearly and deterministically upon the work in the system which meet these objectives reasonably well; with these policies the waiting times are approximately contained in a specified interval a specified fraction of time.

An extremal property of FIFO discipline in G/IFR/1 queues

In a recent paper by Shanthikumar and Sumita (1987), it is conjectured that the ergodic sojourn time of a customer in G/IFR/1 queues is minimized by FIFO (first in, first out) discipline in the sense of increasing and convex ordering. This paper shows that their conjecture is true. In fact, FIFO discipline minimizes for any non-decreasing and convex function f, where N is the (constant) number of arrivals, θ (k) is the customer identity of the kth departing customer, and an and τ n denote the arriving and departing times of the nth customer, respectively.

An extremal property of FIFO discipline in G/IFR/1 queues

In a recent paper by Shanthikumar and Sumita (1987), it is conjectured that the ergodic sojourn time of a customer in G/IFR/1 queues is minimized by FIFO (first in, first out) discipline in the sense of increasing and convex ordering. This paper shows that their conjecture is true. In fact, FIFO discipline minimizes for any non-decreasing and convex function f, where N is the (constant) number of arrivals, θ (k) is the customer identity of the kth departing customer, and an and τ n denote the arriving and departing times of the nth customer, respectively.

A Knockout Switch for Variable-Length Packets

The Knockout Switch is a new packet switch architecture recently proposed for high-speed local and metropolitan area networks, multiprocessor interconnects, and local or toll switches for integrated traffic loads. We describe an approach to extend the original Knockout Switch to work with variable-length packets. This new architecture employs an input broadcast bus arrangement to achieve complete interconnection of the inputs and outputs. Consequently, there is no congestion in the switch fabric other than the unavoidable conflict of multiple simultaneous packets destined for the same output. It is with this output contention that the Knockout principle is fully utilized to efficiently concentrate and store contending packets while maintaining the first-in first-out discipline of the packet sequence; and yet the fabric speed required is no more than the input/output line speeds, Under these design goals, no switch can yield better delay/ throughout performance. These are the most important attributes that have been preserved in the current proposal from the original Knockout Switch. For an N \times N switch configuration, the variable-length packet Knockout Switch consists of N input broadcast buses, and an N:L concentrator ( L \ll N ) and a shared buffer for each output. The design of each subsystem is discussed with emphasis on possible VLSI realization. Using today's technology, we should be able to implement the proposed switch with both input/output lines and internal hardware operating at 50 Mbits/s. The dimension of the switch ( N \times N ) can grow modularly from say 32 × 32 to 1024 × 1024, rendering a total throughput in the range of tens of gigabits per second. Future upgrading of the line interfaces to much higher speed without modification to the internal switch hardware is also possible with a modest restriction on the minimum length of new packets.