Yuming Jiang

A basic stochastic network calculus

A basic calculus is presented for stochastic service guarantee analysis in communication networks. Central to the calculus are two definitions, maximum-(virtual)-backlog-centric (m. b. c) stochastic arrival curve and stochastic service curve, which respectively generalize arrival curve and service curve in the deterministic network calculus framework. With m. b. c stochastic arrival curve and stochastic service curve, various basic results are derived under the (min, +)algebra for the general case analysis, which are crucial to the development of stochastic network calculus. These results include (i)superposition of flows, (ii)concatenation of servers, (iii) output characterization, (iv)per-flow service under aggregation, and (v)stochastic backlog and delay guarantees. In addition, to perform independent case analysis, stochastic strict server is defined, which uses an ideal service process and an impairment process to characterize a server. The concept of stochastic strict server not only allows us to improve the basic results (i)-(v)under the independent case, but also provides a convenient way to find the stochastic service curve of a serve. Moreover, an approach is introduced to find the m.b.c stochastic arrival curve of a flow and the stochastic service curve of a server.

A dynamic bandwidth allocation scheme for differentiated services in EPONs

Passive optical networks bring high-speed broadband access via fiber to the business, curb and home. Among various types of PONs, Ethernet PONs are gaining more and more attention since they are built on widely used Ethernet technology and can offer high bandwidth, low cost and broad services. EPONs use a point-to-multipoint topology, in which multiple optical network units share one uplink channel to transmit multimedia traffic to a control element, the optical line terminal. To avoid data collision on the shared uplink channel, a key issue in EPONs is a contention-free MAC protocol for the OLT to schedule the transmission order of different ONUs. In this article we first review some DBA schemes available in the literature, then propose a two-layer bandwidth allocation scheme that implements weight based priority for this need. To maximally satisfy the requests of all ONUs and provide differentiated services, an ONU is allowed to request bandwidth for all its available traffic, and all traffic classes proportionally share the bandwidth based on their instantaneous demands. The weight set for each class not only prevents high-priority traffic from monopolizing the bandwidth under heavy load but also ensures a minimum bandwidth allocated to each traffic class.

Stochastic Performance Analysis of a Wireless Finite-State Markov Channel

Wireless networks are expected to support a diverse range of quality of service requirements and traffic characteristics. This paper undertakes stochastic performance analysis of a wireless finite-state Markov channel (FSMC) by using stochastic network calculus. Particularly, delay and backlog upper bounds are derived directly based on the analytical principle behind stochastic network calculus. Both the single user and multi-user cases are considered. For the multi-user case, two channel sharing methods among eligible users are studied, i.e., the even sharing and exclusive use methods. In the former, the channel service rate is evenly divided among eligible users, whereas in the latter, it is exclusively used by a user randomly selected from the eligible users. When studying the exclusive use method, the problem that the state space increases exponentially with the user number is addressed using a novel approach. The essential idea of this approach is to construct a new Markov modulation process from the channel state process. In the new process, the multi-user effect is equivalently manifested by its transition and steady-state probabilities, and the state space size remains unchanged even with the increase of the user number. This significantly reduces the complexity in computing the derived backlog and delay bounds. The presented analysis is validated through comparison between analytical and simulation results.

Analysis on generalized stochastically bounded bursty traffic for communication networks

We introduce the concept of generalized stochastically bounded burstiness (gSBB) for Internet traffic, the tail distribution of whose burstiness can be bounded by a decreasing function in a function class with few restrictions. This new concept extends the concept of stochastically bounded burstiness (SBB) introduced by previous researchers to a much larger extent - while the SBB model can apply to Gaussian self-similar input processes, such as fractional Brownian motion, gSBB traffic contains non-Gaussian self-similar input processes, such as /spl alpha/-stable self-similar processes, which are not SBB in general. We develop a network calculus for gSBB traffic. We characterize gSBB traffic by the distribution of its queue size. We explore the property of sums of gSBB traffic and the relation of input and output processes. We apply this calculus to a work-conserving system shared by a number of gSBB sources, to analyze the behavior of output traffic for each source and to estimate the probabilistic bounds for delays. We expect this new calculus to be of particular interest in the implementation of services with statistical qualitative guarantees.

A probabilistic preemptive scheme for providing service differentiation in OBS networks

In this paper, we propose a probabilistic preemptive (PP) scheme for service differentiation in optical burst switching (OBS) networks. By changing the preemptive probability, an OBS node can adjust the ratio of burst blocking probability between different traffic classes, while the overall blocking probability is not affected.

Analysis of stochastic service guarantees in communication networks: a server model

Many communication networks such as wireless networks only provide stochastic service guarantees. For analyzing stochastic service guarantees, research efforts have been made in the past few years to develop stochastic network calculus, a probabilistic version of (min, +) deterministic network calculus. However, many challenges have made the development difficult. Some of them are closely related to server modeling, which include output characterization, concatenation property, stochastic backlog guarantee, stochastic delay guarantee, and per-flow service under aggregation. In this paper, we propose a server model, called stochastic service curve to facilitate stochastic service guarantee analysis. We show that with the concept of stochastic service curve, these challenges can be well addressed. In addition, we introduce strict stochastic server to help find the stochastic service curve of a stochastic server, which characterizes the service of the server by two stochastic processes: an ideal service process and an impairment process.

Approximate Consensus in Stochastic Networks With Application to Load Balancing

This paper is devoted to the approximate consensus problem for stochastic networks of nonlinear agents with switching topology, noisy, and delayed information about agent states. A local voting protocol with nonvanishing (e.g., constant) step size is examined under time-varying environments of agents. To analyze dynamics of the closed-loop system, the so-called method of averaged models is used. It allows us to reduce analysis complexity of the closed-loop stochastic system. We derive the upper bounds for mean square distance between states of the initial stochastic system and its approximate averaged model. These upper bounds are used to obtain conditions for approximate consensus achievement. An application of general theoretical results to the load balancing problem in stochastic dynamic networks with incomplete information about the current states of agents and with changing set of communication links is considered. The conditions to achieve the optimal level of load balancing are established. The performance of the system is evaluated both analytically and by simulation.

A calculus for stochastic QoS analysis

The issue of Quality of Service (QoS) performance analysis in packet-switched networks has drawn a lot of attention in the networking community. There is a lot of work including an elegant theory under the name of network calculus, which focuses on analysis of deterministic worst case QoS performance bounds. In the meantime, researchers have studied stochastic QoS performance for specific schedulers. However, most previous works on deterministic QoS analysis or stochastic QoS analysis have only considered a server that provides deterministic service, i.e. deterministically bounded rate service. Few have considered the behavior of a stochastic server that provides input flows with variable rate service, for example wireless links. In this paper, we propose a stochastic network calculus to analyze the end-to-end stochastic QoS performance of a system with stochastically bounded input traffic over a series of deterministic and stochastic servers. We also prove that a server serving an aggregate of flows can be regarded as a stochastic server for individual flows within the aggregate. Based on this, the proposed framework is further applied to analyze per-flow stochastic QoS performance under aggregate scheduling.

Queueing processes in GPS and PGPS with LRD traffic inputs

Long range dependent (LRD) traffic whose single server queue process is Weibull Bounded (WB) is first analyzed. Two upper bounds on the individual sessions queue length of LRD traffic under the generalized processor sharing (GPS) scheduling discipline are then contributed. It is shown that the index parameter in the upper bound of one LRD flow, (in addition to the decay rate and the asymptotic constant), may be affected by other LRD flows. A new concept, called LRD isolation, is subsequently contributed and accompanying it, a new technique is contributed to check whether a flow, with a given GPS weight assignment, can be guaranteed to be LRD isolated. This technique is also amenable for use in an online call admission control (CAC) scenario. When existing flows have already been assigned contract weights that cannot be changed, our technique can be used to determine minimum contract weights to be assigned to a new flow in order to guarantee the flow to be LRD isolated. The results are also extended to a PGPS (packet-based GPS) scheduler and relevant numerical results are provided to show the usefulness of our bounds and LRD isolation technique.

An approximation for waiting time tail probabilities in multiclass systems

This article proposes a simple exponential approximation for waiting time tail probabilities in multiclass systems. The approximation is evaluated by making comparisons with simulation results, which show that the proposed approximation is adequate.