Delay Analysis of a HOL Priority Queue

The integration of different types of traffic in packet-based networks spawns the need for traffic differentiation. In this tutorial paper, we present some analytical techniques to tackle discrete-time queueing systems with priority scheduling. We investigate both preemptive (resume and repeat) and non-preemptive priority scheduling disciplines. Two classes of traffic are considered, high-priority and low-priority traffic, which both generate variable-length packets. A probability generating functions approach leads to performance measures such as moments of system contents and packet delays of both classes.KeywordsService TimePacket DelayPriority QueueSystem ContentPriority ScheduleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

System delay versus system content for discrete-time queueing systems subject to server interruptions

In high speed networks, the strict priority (SP) scheduling discipline is perhaps the most common and simplest method to schedule packets from different classes of applications, each with diverse performance requirements. With this discipline, however, packets at higher priority levels can starve packets at lower priority levels. To resolve this starvation problem, we propose to assign a parameter to each priority queue in the SP discipline. The assigned parameter determines the probability with which its corresponding queue is served when the queue is polled by the server. We thus form a new packet scheduling discipline, referred to as the probabilistic priority (PP) discipline. By properly setting the assigned parameters, service differentiation as well as fairness among traffic classes can be achieved in PP. In addition, the PP discipline can be easily reduced to the ordinary SP discipline or to the reverse SP discipline.

According to the characteristics of data in coalmine industrial Ethernet ring networks and in order to guarantee the demand of the real-time data in it, a hybrid scheduling method with non-preemptive priority and EDF scheduling method based on the IEEE802.1p protocol is proposed in the switch. We calculate the maximum transmitting delay of the real-time data using network calculus theory. The result shows that EDF decreases transmission delay for non-periodic data better than FCFS by theoretical computation and simulation.

The operation of digital systems are based on time slotting and it finds many applications particularly in communication networks. It is important to analyze a digital network on some digital concepts. In this paper we analyze the network buffer through discrete time queueing system in which queue is discrete in nature and it is used to analyze the performance of the communication networks buffer. Discrete time models can be used to represents such type of systems in terms of slotted time units to models any physical system. More than one state changes in discrete time models from one time unit to another. Discrete time markov chains are used to describes the behavior of the network under the specific conditions and various performance measures are evaluated such as queue length, mean waiting time and mean number in the system.

This paper discusses a discrete-time queueing system in which an arriving customer may adopt four different strategies; two of them correspond to a LCFS discipline where displacements or expulsions occur, and in the other two, the arriving customer decides to follow a FCFS discipline or to become a negative customer eliminating the customer in the server, if any. The different choices of the involved parameters make this model to enjoy a great versatility, having several special cases of interest. We carry out a thorough analysis of the system, and using a generating function approach, we derive analytical results for the stationary distributions obtaining performance measures for the number of customers in the queue and in the system. Also, recursive formulae for calculating the steady-state distributions of the queue and system size has been developed. Making use of the busy period of an auxiliary system, the sojourn times of a customer in the queue and in the system have also been obtained. Finally, some numerical examples are given.

A well-known problem with priority policies is starvation of delay-tolerant traffic. Additionally, insufficient control over delay differentiation (which is needed for modern network applications) has incited the development of sophisticated scheduling disciplines. The priority policy we present here has the benefit of being open to rigorous analysis. We study a discrete-time queueing system with a single server and single queue, in which $N$ types of customers enter pertaining to different priorities. A general i.i.d. arrival process is assumed and service times are generally distributed. We divide the time axis into 'frames' of fixed size (counted as a number of time-slots), and reorder the customers that enter the system during the same frame such that the high-priority customers are served first. This paper gives an analytic approach to studying such a system, and in particular focuses on the system content (meaning the customers of each type in the system at random slotmarks) in stationary regime, and the delay distribution of a random customer. Clearly, in such a system the frame's size is the key factor in the delay differentiation between the $N$ priority classes. The numerical results at the end of this paper illustrate this observation.

Achieving differentiated services through multi-class probabilistic priority scheduling

A well-known problem with priority policies is starvation of delay-tolerant traffic. Furthermore insufficient control over delay differentiation (which is needed for modern network applications) has incited the development of other scheduling disciplines. Processor sharing is one of many solutions to this problem. The priority policy we present here has the added benefit of being more open to rigorous analysis. We study a discrete-time queueing system with a single server and single queue, in which N types of customers enter (we will refer to packets as customers) pertaining to different priorities. A general i.i.d. arrival process is assumed and service times are deterministic. We divide the time axis into 'frames' of fixed size (counted as a number of time-slots), and reorder the customers that enter the system during the same frame such that the high-priority customers are served first. This paper gives an analytic approach to studying such a system, and in particular focuses on the queue content (meaning the customers of each type in the system at random slotmarks) in stationary regime. Clearly the frame's size is the key factor in the delay differentiation between the two priority classes. The numerical results at the end of this paper illustrate this fact.

Queueing models can be used to model and analyze the performance of various subsystems in telecommunication networks; for instance, to estimate the packet loss and packet delay in network routers. Since time is usually synchronized, discrete-time models come natural. We start this paper with a review of suitable discrete-time queueing models for communication systems. We pay special attention to two important characteristics of communication systems. First, traffic usually arrives in bursts, making the classic modeling of the arrival streams by Poisson processes inadequate and requiring the use of more advanced correlated arrival models. Second, different applications have different quality-of-service requirements (packet loss, packet delay, jitter, etc.). Consequently, the common first-come-first-served (FCFS) scheduling is not satisfactory and more elaborate scheduling disciplines are required. Both properties make common memoryless queueing models (M/M/1-type models) inadequate. After the review, we therefore concentrate on a discrete-time queueing analysis with two traffic classes, heterogeneous train arrivals and a priority scheduling discipline, as an example analysis where both time correlation and heterogeneity in the arrival process as well as non-FCFS scheduling are taken into account. Focus is on delay performance measures, such as the mean delay experienced by both types of packets and probability tails of these delays.

In this paper, the waiting time and response time processes in continuous-time two parallel queueing systems are analyzed as well as the system size process in discrete-time two parallel queueing systems. Upon arrival, each job splits into two tasks, denoted by task 1 and task 2. Task k, $k = 1,2$, is assigned to the kth queueing system to be served on a FCFS (first-come-first-served) basis. Each queueing system consists of a single server and an infinite-capacity queue. For the continuous-time queueing system, we assume that jobs arrive in a state-independent Poisson fashion with rate $\lambda $; the servers have exponential service times with rates $\mu _1 $ and $\mu _2 $, respectively. A closed-form expression for the Laplace transform of the ergodic bivariate waiting time distribution is derived. The distribution of the sum of the two waiting times is then obtained. The distribution of the response time when $\mu _1 = \mu _2 $ is derived analytically. For the discrete-time queueing systems, it is assu...

One of the typical error control schemes used in data transmission systems is the selective-repeat ARQ. Previously, the transmission delay for this scheme has been analyzed mostly for an independent error channel. In practice, however, the state of the channel varies with time so that error generation is not independent. This paper considers a non-independent error channel and analyzes transmission delay performance for a selective-repeat ARQ scheme. An error model is used in which the change of the channel state is represented as a 2-state Markov chain. A strict analysis is applied using a discrete-time queuing system and the transmission delay distribution for the frame is derived. When the round-trip propagation delay or the frame queue length is increased, however, a large amount of computation is required in order to obtain the numerical result due to enlargement of the state space. In order to simplify the numerical calculation we give an approximate analysis for the case where the propagation delay or the frame queue length is increased. The average transmission delay is discussed based on numerical examples. As a result, we show that the average transmission delay performance is significantly improved when the decay factor of the Markov chain approaches zero from positive values. © 1998 Scripta Technica. Electron Comm Jpn Pt 1, 81(6): 31–41, 1998

A performance analysis of discrete-time tandem queues with Markovian sources

We develop and analyze simple algorithms for scheduling multicast traffic in wavelength division multiplexing (WDM) broadcast-and-select networks with N nodes, W wavelengths, and a single receiver per node that can be tuned to any of the W wavelengths. Each message is addressed to /spl kappa/ randomly chosen nodes. Since optimal message scheduling in a WDM network is known to be very difficult, we study two simple scheduling schemes: in the first, a message is continuously retransmitted until it is received by all of its intended recipients; and in the second, a random delay is introduced between retransmissions of the same message. We develop a throughput analysis for both schemes using methods from discrete-time queueing systems and show that the algorithm with random delays between retransmissions results in higher throughput. We also consider a number of receiver algorithms for selecting among multiple simultaneous transmissions and show, through simulation, that an algorithm where the receiver selects the message with the least number of intended recipients performs better than a random selection algorithm. Finally, we show that channel utilization can be significantly increased with multiple receivers/node.

Performance evaluation of CAI and RAI transmission modes in a GI-G-1 queue