Queueing models for the analysis of communication systems

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.

Session-based arrival streams are a new approach for modelling the traffic generated by users in a telecommunication network. In this paper, we analyze the behavior of a discrete-time buffer with one output line, an infinite storage capacity and session-based arrivals. Users from an infinite user population can start and end sessions during which they are active and send packets to the buffer. Each active user generates a random but strictly positive number of packets per time slot. Unlike in previous work, there are T different session types and for each type, the session-length distribution is general. The resulting discrete-time queueing model is analyzed by means of an analytical technique, which is basically a generating-functions approach that uses an infinite-dimensional state description. Expressions are obtained for the steady-state probability generating functions of both the buffer content and the packet delay. From these, the mean values and the tail distributions of the buffer content and the packet delay are derived as well. Some numerical examples are shown to illustrate the influence of the session-based packet arrival process on the buffer behavior.

A discrete-time multi-server queueing model for opportunistic spectrum access systems

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 shows that the analysis and the design of discrete-time models of continuous-time systems can be carried out within a single framework. Briefly, all classes of discrete-time models, namely the invariant models, the mapping models and the matched pole-zero models, are shown to incorporate the common structure of a hold followed by a continuous-time system and the ideal sampler. This interpretation of discrete-time models of continuous-time systems facilitates the understanding of the differences and similarities among the various discrete-time models. A numerical example illustrates the concepts involved.

This paper provides two different discrete-time finite-buffer queueing models of the G 1 [X] +G2/D/1/s-type for modelling CAC in ATM. In the G 1 [X] +G2-input, G1 and G2 produce (correlated) interarrival times and the independent r.v. X generates the size of the batch arriving, when G1 produces an arrival. Thus, this model represents the situation, when a new connection (G2) is admitted, i.e. superimposed to already existing traffic (G 1 [X] ) in an ATM-switch. The first model -given in detail here- is based on Neuts’ M/G/1-type paradigm, and allows the solution of the queueing model for a DBMAP+DMAP input including the DMAP 1 [X] +DMAP2 case (also for a general service process). Per-stream probability functions (p.f.’s) of the occupancy and loss probabilities can be computed. The second model is based on the unfinished work and allows to compute per-stream loss probabilities, occupancy and waiting-time p.f.’s, as well as, for stream 2, an exact value of the conditional loss probability that given a cell of stream 2 is lost, the next cell of stream 2 is also lost. Since the DMAP 1 [X] +DMAP2-input can be handled by both methods, an analytical validation of the results is possible, which typically only differ in the last 4 of 16 figures (using double-precision-numbers in a C-program). Both models allow service times higher than the time-unit, which is necessary for a correct description of a multiplexer’s behaviour, when the output line is slower than the input lines. Numerical results show that positive correlation in one stream can have a significant negative influence on QOS parameters of both streams so that effective bandwidth does better than sigma rule, since it inherently carries some estimate of correlation.

<p>Software-Defined-Networking (SDN) simplifies the configuration complexity in the computer communication network by decoupling the control plane from the data plane in a switch. In SDN, the switch has the data plane only and is configured by the logically centralised controller which simplifies the forwarding of packets in the network. However, an SDN switch is sensitive to delay and loss of packets which significantly affects the network performance. This thesis uses queueing theory to conduct modelling and performance analysis of OpenFlow-based SDN switches. OpenFlow is the de-facto protocol for communication between an SDN switch and the controller. Using queueing theory, three aspects of packet processing in an SDN switch are explored. First, the existing research has primarily modelled the output buffer of an SDN switch using two buffer sharing mechanisms: the single shared buffer and the priority buffer. However, the effect of buffer dimensioning in these buffer sharing mechanisms has not been investigated. Buffer dimensioning helps in determining the minimum buffer capacity for a desired loss probability. The research in this thesis shows that the use of priority buffer in an SDN switch reduces the time to update flow tables than the shared buffer but at the cost of a higher buffer capacity. Second, much of the existing research has not investigated the impact of internal buffering of data packets whereby a fraction of a data packet header is sent to the controller instead of an entire data packet. To investigate the impact of internal buffering, the queueing model for an SDN switch with the internal buffer is developed. The investigation shows that at the time of congestion, the internal buffer in an SDN switch improves the network performance with lower delay and lower packet loss. Finally, existing research has focused on a software switch in SDN and very little research has studied the performance of a hardware switch. To characterise the performance of SDN-based hardware and software switches and identify the tradeoffs between them, a unified queueing model has been developed. The unified queueing model is an analytical tool for network engineers to predict delay and packet loss in their SDN deployments. The analysis shows the benefits of a hardware switch over a software switch. These benefits are lower delay and lower packet loss. However, the increasing involvement of the controller reduces the benefit of using a hardware switch, i.e. forwarding packets at the line speed rate. This research guides network designers and analysts in the selection of the shared or buffer model for an SDN switch for their desired Quality of Service (QoS). Furthermore, the developed queueing model for an SDN switch with the internal buffer studies the impact of internal buffering in an SDN switch. Finally, the unified queueing model helps in the selection of a software or hardware switch in SDN.</p>

For several specific queueing models with a vacation policy, the stationary system occupancy at the beginning of a random slot is distributed as the sum of two independent random variables. One of these variables is the stationary number of customers in an equivalent queueing system with no vacations. For models in continuous time with Poissonian arrivals, this result is well-known, and referred to as stochastic decomposition, with proof provided by Fuhrmann and Cooper. For models in discrete time, this result received less attention, with no proof available to date. In this paper, we first establish a proof of the decomposition result in discrete time. When compared to the proof in continuous time, conditions for the proof in discrete time are somewhat more general. Second, we explore four different examples: non-preemptive priority systems, slot-bound priority systems, polling systems, and fiber delay line (FDL) buffer systems. The first two examples are known results from literature that are given here as an illustration. The third is a new example, and the last one (FDL buffer systems) shows new results. It is shown that in some cases the queueing analysis can be considerably simplified using this decomposition property.

Online monitoring of multimedia networks is required to ensure seamless and ubiquitous delivery of services to the end users. Quality of multimedia content, such as video streams, often gets degraded due to network losses such as packet loss. Frame freezing artifacts are introduced in a video stream when packet loss or packet delay takes place. Estimating the perceptual impact of these artifacts on quality of experience of end users helps service providers to maintain quality of service. In this paper, we have presented a novel no-reference video quality metric, which measures the impact of frame freezing due to packet loss and delay in video streaming networks. The proposed metric is based on several features that directly impact the quality of experience of end users. These features, including motion characteristics of videos, are calculated using the temporal information between video frames and then combined mathematically to form a video quality metric. Different weights are assigned to different features for better performance of the proposed metric. With detailed experiments, we have shown that our method outperforms other contemporary methods in terms of high accuracy and low computation time in frame freeze detection, low root mean square values, high coefficient of determination, and high correlation between subjective and objective measurements. We have used five video databases for our model's evaluation and validation. Furthermore, we have shown that our method is statistically superior to the other models in comparison.

Construction of discrete-time models for port-controlled Hamiltonian systems with applications

The analysis of system performance measures is fairly simple if there is only one or several channels with identical service times and arranged in parallel with exponentially distributed inter arrival time of packets and service time. However, heterogeneous multiple channels often occur in practice and here the channels have different service times. It is therefore useful to be able to calculate the performance measures of such systems. We shall take an exact analytical model of the asymmetric data network node and assume that the arrival process is Poisson of two priority flows with different rates and two channels with different service times distributed exponentially and in case with determine service time. In symmetric queuing systems, the response time depends only on whether an arrival message finds some free channel. An asymmetric multiple channel system differs since which of the channels processes the message. It is very important to take analysis of different strategies for selecting a free channel. In a system with heavy traffic there is usually all channels are occupied and therefore a channel selection strategy is not so efficient. The transmission order is from high-priority packet to low-priority packet. Two priority packets queues share a limited size single buffer. The each priority packet is dropped if the queue length exceeds a capacity of buffer. Network node performance measures such as packet losses, packet delay, channel utilization are evaluated by means of analytical and simulation models. Some calculated system performance measures results are presented in figures.

A multiserver discrete-time buffer system is studied. Packets arrive in the system according to a general correlated process, which is not further specified. The service times of the packets are of constant length. Explicit expressions are derived for the distribution, the probability generating function, and the mean and variance of the packet delay, in terms of the distribution, the probability generating function, and the mean and variance of the buffer contents. It is observed that knowledge of the exact nature of the arrival process is not required to be able to derive these relationships between the statistics of the delay and the occupancy. >

Performance evaluation of prioritized scheduling with buffer management for differentiated services architectures

Switching funnel transformation function-based discrete-time sliding-mode control for servo systems with time-varying external disturbances

Priority scheduling for packets is a hot topic, as interactive (voice, video) services are being integrated in existing data networks. In this paper, we consider a discrete-time queueing system with a non-preemptive (or Head-Of-the-Line) priority scheduling discipline and a general number of priority classes. Packets of variable length arrive in the queueing system. We derive expressions for the probability generating functions of the packet delays. From these functions, some performance measures (such as moments and approximate probabilities) are calculated. We illustrate the performance measures by means of some numerical examples and show how to apply the theoretical results to a queue that handles arriving multimedia traffic.