Analysis of Discrete-Time Buffers with General Session-Based Arrivals

Distributed algorithms such as CSMA provide a popular mechanism for sharing the transmission medium among competing users in large-scale wireless networks. Conventional models for CSMA that are amenable for analysis assume that users always have packets to transmit. In contrast, when users do not compete for medium access when their buffers are empty, a complex interaction arises between the activity states and the buffer contents. We develop a meanfield approach to investigate this dynamic interaction for networks with many users. We identify a time-scale separation between the evolution of the activity states and the buffer contents, and obtain a deterministic dynamical system describing the network dynamics on a macroscopic scale. The fixed point of the dynamical system yields highly accurate approximations for the stationary distribution of the buffer contents and packet delay, even when the number of users is relatively moderate.

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.

This paper presents the large-buffer asymptotics for a multiplexer which serves N types of heterogeneous sessions which have long-tailed session lengths. Specifically, the model considered is that sessions of type i ∈ {1,…,N} arrive as a Poisson process with rate λ i . Each type of session (independently) remains active for a random duration, say τ i , where P(τ i > x) ~ α i x -(1 + β i ) for positive numbers α i and β i . While active, a session transmits at a rate r i . Under the assumption that the average load ρ = ∑ N i=1 r i λ i E[τ i ] < C, where C denotes the server capacity, we show that both the tail distribution of the stationary buffer content and the loss asymptotics in finite buffers of size z behave approximately as z -κ J 0 , where κ J 0 depends not only on the β i but also on the transmission rates r i ; it is the ratio of β i to r i which determines κ J 0 . When specialized to the homogeneous case, i.e., when r i =r and β i = β for all i, the result coincides with results reported in the literature which have been shown under more restrictive hypotheses. Finally, it is a simple observation that light-tailed sessions only have the effect of reducing the available capacity for long-tailed sessions, but do not contribute otherwise to the definition of κ J 0 .

Studies the performance of a statistical multiplexer, to which messages composed of a variable number of fixed-length packets arrive at the rate of one packet per slot (train arrivals), resulting in a correlated packet arrival stream. The distribution of the message lengths is general. The system is analyzed by using an infinite-dimensional state description and a generating-functions approach. An explicit expression is obtained for the probability generating function (pgf) of the queue length and the packet delay. Also, closed-form expressions are derived for the mean and the tail distribution of the queue length and the packet delay. The mean message waiting time is obtained as well. The buffer behavior with train arrivals is compared to that with batch arrivals, where all the packets of a message enter the buffer during the same slot. By means of some numerical examples, the impact of the message-length distribution on the multiplexer performance is investigated.

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.

We establish mean-field limits for large-scale random-access networks with buffer dynamics and arbitrary interference graphs. Although saturated buffer scenarios have been widely investigated and yield useful throughput estimates for persistent sessions, they fail to capture the fluctuations in buffer contents over time and provide no insight in the delay performance of flows with intermittent packet arrivals. Motivated by that issue, we explore in the present paper random-access networks with buffer dynamics, where flows with empty buffers refrain from competition for the medium. The occurrence of empty buffers thus results in a complex dynamic interaction between activity states and buffer contents, which severely complicates the performance analysis. Hence, we focus on a many-sources regime where the total number of nodes grows large, which not only offers mathematical tractability but is also highly relevant with the densification of wireless networks as the Internet of Things emerges. We exploit timescale separation properties to prove that the properly scaled buffer occupancy process converges to the solution of a deterministic initial value problem and establish the existence and uniqueness of the associated fixed point. This approach simplifies the performance analysis of networks with huge numbers of nodes to a low-dimensional fixed-point calculation. For the case of a complete interference graph, we demonstrate asymptotic stability, provide a simple closed form expression for the fixed point, and prove interchange of the mean-field and steady-state limits. This yields asymptotically exact approximations for key performance metrics, in particular the stationary buffer content and packet delay distributions.

We consider two parallel, infinite capacity, M/G/1 queues characterized by ( U_{1}(t), U_{2}(t) ) with U_{j}(t) denoting the unfinished work (buffer content) in queue j . A new arrival is assigned to the queue with the smaller buffer content. We construct formal (as opposed to rigorous) asymptotic approximations to the Joint stationary distribution of the Markov process ( U_{1}(t), U_{2}(t) ), treating separately the asymptotic limits of heavy traffic, light traffic, and large buffer contents. In heavy traffic, the stochastic processes U_{1}(t) + U_{2}(t) and U_{2}(t) - U_{1}(t) become independent, with the distribution of U_{1}(t) + U_{2}(t) identical to the heavy traffic waiting time distribution in the standard M/G/2 queue, and the distribution of U_{2}(t) - U_{1}(t) closely related to the tail of the service time density. In light traffic, we obtain a formal expansion of the stationary distribution in powers of the arrival rate.

Port partitioning and dynamic queueing for IP forwarding

Session types allow communication protocols to be specified type-theoretically so that protocol implementations can be verified by static type-checking. We extend previous work on session types for distributed object-oriented languages in three ways. (1) We attach a session type to a class definition, to specify the possible sequences of method calls. (2) We allow a session type (protocol) implementation to be modularized , i.e. partitioned into separately-callable methods. (3) We treat session-typed communication channels as objects, integrating their session types with the session types of classes. The result is an elegant unification of communication channels and their session types, distributed object-oriented programming, and a form of typestates supporting non-uniform objects, i.e. objects that dynamically change the set of available methods. We define syntax, operational semantics, a sound type system, and a correct and complete type checking algorithm for a small distributed class-based object-oriented language. Static typing guarantees that both sequences of messages on channels, and sequences of method calls on objects, conform to type-theoretic specifications, thus ensuring type-safety. The language includes expected features of session types, such as delegation, and expected features of object-oriented programming, such as encapsulation of local state. We also describe a prototype implementation as an extension of Java.

Distributed processing through ad hoc and sensor networks is having a major impact on scale and applications of computing. The creation of new cyber-physical services based on wireless sensor devices relies heavily on how well communication protocols can be adapted and optimized to meet quality constraints under limited energy resources. The IEEE 802.15.4 medium access control protocol for wireless sensor networks can support energy efficient, reliable, and timely packet transmission by a parallel and distributed tuning of the medium access control parameters. Such a tuning is difficult, because simple and accurate models of the influence of these parameters on the probability of successful packet transmission, packet delay, and energy consumption are not available. Moreover, it is not clear how to adapt the parameters to the changes of the network and traffic regimes by algorithms that can run on resource-constrained devices. In this paper, a Markov chain is proposed to model these relations by simple expressions without giving up the accuracy. In contrast to previous work, the presence of limited number of retransmissions, acknowledgments, unsaturated traffic, packet size, and packet copying delay due to hardware limitations is accounted for. The model is then used to derive a distributed adaptive algorithm for minimizing the power consumption while guaranteeing a given successful packet reception probability and delay constraints in the packet transmission. The algorithm does not require any modification of the IEEE 802.15.4 medium access control and can be easily implemented on network devices. The algorithm has been experimentally implemented and evaluated on a testbed with off-the-shelf wireless sensor devices. Experimental results show that the analysis is accurate, that the proposed algorithm satisfies reliability and delay constraints, and that the approach reduces the energy consumption of the network under both stationary and transient conditions. Specif- cally, even if the number of devices and traffic configuration change sharply, the proposed parallel and distributed algorithm allows the system to operate close to its optimal state by estimating the busy channel and channel access probabilities. Furthermore, results indicate that the protocol reacts promptly to errors in the estimation of the number of devices and in the traffic load that can appear due to device mobility. It is also shown that the effect of imperfect channel and carrier sensing on system performance heavily depends on the traffic load and limited range of the protocol parameters.

A Fluid queue is a mathematical model used to describe fluid level in a reservoir subject to randomly determined periods of filling and emptying the system without interruption called a buffer, according to a randomly varying rate regulated by an external stochastic environment. Such fluid queues are used as a mathematical tool for modeling, for example, to approximate discrete models, model the spread of wildfires in ruin theory and to model high speed data networks, a router, computer networks including call admission control, traffic shaping and modeling of TCP and production and inventory systems. The fluid from the first phase (i.e, fluid output of the queue) goes to the second phase represents a buffer with a constant leak rate c. We always assume that service rate is greater than buffer, μ ˃ c. In this paper, a fluid queue driven by infinite queue with fixed –size batch arrivals. The generating function technique is used to obtain the expressions for steady-state distribution of both the buffer content and stationary state probabilities of background birth-death process. Hence, the performance measures are computed whereas the server utilization analysis and mean buffer content are investigated. . In addition, some numerical results are provided to illustrate the effect of various parameters on the distribution of the buffer content.

Many important factors affect the spread of childhood infectious disease. To better understand the fundamental drivers of infectious disease spread, several researchers have estimated seasonal transmission coefficients in discrete-time models. In this paper, we build upon this previous work and also develop a framework for efficient estimation using continuous differential equation models. We introduce nonlinear programming formulations to efficiently estimate model parameters and seasonal transmission profiles from existing case count data for the childhood disease, measles. We compare results from discrete time and continuous time models and address several shortcomings of the discrete-time method, including removing the need for the data reporting interval to match the time between successive cases in the chain of transmission or serial interval of the disease. Using a simultaneous approach for optimization of differential equation systems, we demonstrate that seasonal transmission parameters can be effectively estimated using continuous time models instead of discrete-time models.

Wireless Local Area Networks (WLAN)s are today common for access to Internet; well-known and used is IEEE 802.11 standardized technology. Some drawbacks of the standardized distributed medium access scheme, Distributed Coordination Function (DCF) has resulted in considerations made to extend the DCF from single-hop communications to multi-hop. Multihopping has the potential to reduce energy consumption and increase throughput and coverage. The drawback is lack of Quality-of-Service (QoS) support, which already with single-hop communication was bad, but extending a communication between two peers to multi-hop significantly reduces the possibility to offer reliable transmissions. The contention-based medium access performed at each hop with the DCF results in large uncertainties as to when a packet arrives to its end-destination. There are two general approaches for extending the DCF with QoS functionality: 1. Allocate resources for a flow and 2. Assign a flow higher priority than other flows. My hypothesis is that for strict QoS guarantees, a reservation-based approach is the better one. This has been my motivation to design a new medium access protocol; based on the DCF, periodic time slots for QoS-demanding real-time applications are reserved. The Distributed Allocation of time slots for Real-time traffic (DARE) is unique as it totally distributed sets up an end-to-end reservation before the transmission of data begins, repairs broken reservations, support many periods and time slot sizes and distribute piggy-backed information even to a two-hop radius from a receiver. This thesis describes the DARE protocol and also presents results from comparisons of DARE, DCF and the IEEE 802.11 E standardized priority-based QoS medium access protocol Enhanced Distributed Channel Access (EDCA). Using simulations, this thesis shows that DARE offers constant end-to-end packet delay for a flow, very low average packet delay in the whole system and constant throughput. EDCA and DCF depend strongly on the total network load; average packet delay for a real-time flow increases rapidly with the surrounding load. DARE outperforms both DCF and EDCA when many flows are present, even in networks with frequent topology changes where reservations must be repaired. Thus, the reservation-based DARE protocol is the most suitable approach for extending DCF with QoS.

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.

On the reversibility of manufacturing networks