Large deviation asymptotics for occupancy problems

In the standard formulation of the occupancy problem one considers the distribution of r balls in n cells, with each ball assigned independently to a given cell with probability 1/n. Although closed form expressions can be given for the distribution of various interesting quantities (such as the fraction of cells that contain a given number of balls), these expressions are often of limited practical use. Approximations provide an attractive alternative, and in the present paper we consider a large deviation approximation as r and n tend to infinity. In order to analyze the problem we first consider a dynamical model, where the balls are placed in the cells sequentially and ``time'' corresponds to the number of balls that have already been thrown. A complete large deviation analysis of this ``process level'' problem is carried out, and the rate function for the original problem is then obtained via the contraction principle. The variational problem that characterizes this rate function is analyzed, and a fairly complete and explicit solution is obtained. The minimizing trajectories and minimal cost are identified up to two constants, and the constants are characterized as the unique solution to an elementary fixed point problem. These results are then used to solve a number of interesting problems, including an overflow problem and the partial coupon collector's problem.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000013

T-WAS and T-XAS algorithms for fiber-loop optical buffers

In optical packet/burst switched networks fiber loops provide a viable and compact means of contention resolution. For fixed size packets it is known that a basic void-avoiding schedule (VAS) can vastly outperform a more classical pre-reservation algorithm as FCFS. For the setting of a uniform distributed packet size and a restricted buffer size we proposed two novel forward-looking algorithms, WAS and XAS, that, in specific settings, outperform VAS up to 20% in terms of packet loss. This contribution extends the usage and improves the performance of the WAS and XAS algorithms by introducing an additional threshold variable. By optimizing this threshold, the process of selectively delaying packet longer than strictly necessary can be made more or less strict and as such be fitted to each setting. By Monte Carlo simulation it is shown that the resulting T-WAS and T-XAS algorithms are most effective for those instances where the algorithms without threshold can offer no or only limited performance improvement

On the highly stable performance of loss-free optical burst switching networks

Increase of bandwidth demand in data networks, driven by the continuous growth of the Internet and the increase of bandwidth greedy applications, raise the issue of how to support all the bandwidth requirements in the near future. Three optical switching paradigms have been defined and are being investigated: Optical Circuit Switching (OCS); Optical Packet Switching (OPS); and Optical Burst Switching (OBS). Among these paradigms, OBS is seen as the most appropriate solution today. However, OBS suffers from high burst loss as a result of contention in the bufferless mode of operation. This issue was investigated by Coutelen et al., 2009 who proposed the loss-free CAROBS framework whereby signal convertors of the optical signal to the electrical domain ensure electrical buffering. Convertors increase the network price which must be minimized to reduce the installation and operating costs of the CAROBS framework. An analysis capturing convertor requirements, with respect to the number of merging flows and CAROBS node offered load, was carried out. We demonstrated the convertor location significance, which led to an additional investigation of the shared wavelength convertors scenario. Shared wavelength convertors significantly decrease the number of required convertors and show great promise for CAROBS. Based on this study we can design a CAROBS network to contain a combination of simple and complex nodes that include none or some convertors respectively, a vital feature of network throughput efficiency and cost

SOA-Based Optical Packet Switching Architectures

The service evolution and the rapid increase in traffic levels fuel the interest toward switching paradigms enabling the fast allocation of Wavelength Division Multiplexing WDM channels in an on demand fashion with fine granularities (microsecond scales). For this reason, in the last years, different optical switching paradigms have been proposed: optical-packet switching (OPS), optical-burst switching (OBS), wavelength-routed OBS, etc. Among the various all-optical switching paradigms, OPS attracts increasing attention. Owing to the high switching rate, Semiconductor Optical Amplifier (SOA) is a key technology to realize Optical Packet Switches. We propose some Optical Packet Switch (OPS) architectures and illustrate their realization in SOA technology. The effectiveness of the technology in reducing the power consumption is also analyzed. The chapter is organized in three sections. The main blocks (Switching Fabric, Wavelength Conversion stage, Synchronization stage) of an OPS are illustrated in Section 2 where we also show some examples of realizing wavelength converters and synchronizers in SOA technology. Section 3 introduces SOA-based single-stage and multi-stage switching fabrics. Finally the SOA-based OPS power consumption is investigated in Section 4

Upstream traffic capacity of a WDM EPON under online GATE-driven scheduling

Passive optical networks are increasingly used for access to the Internet and it is important to understand the performance of future long-reach, multi-channel variants. In this paper we discuss requirements on the dynamic bandwidth allocation (DBA) algorithm used to manage the upstream resource in a WDM EPON and propose a simple novel DBA algorithm that is considerably more efficient than classical approaches. We demonstrate that the algorithm emulates a multi-server polling system and derive capacity formulas that are valid for general traffic processes. We evaluate delay performance by simulation demonstrating the superiority of the proposed scheduler. The proposed scheduler offers considerable flexibility and is particularly efficient in long-reach access networks where propagation times are high

Retrial Queuing Models of Multi-Wavelength FDL Feedback Optical Buffers

Cataloged from PDF version of article.Optical buffers based on Fiber Delay Lines (FDL) have been proposed for contention resolution in optical packet/burst switching systems. In this article, we propose a retrial queuing model for FDL optical buffers in asynchronous optical switching nodes. In the considered system, the reservation model employed is of post-reservation type and optical packets are allowed to re-circulate over the FDLs in a probabilistic manner. We combine the MMPP-based overflow traffic models of the classical circuit switching literature and fixed-point iterations to devise an algorithmic procedure to accurately estimate blocking probabilities as a function of various buffer parameters in the system when packet arrivals are Poisson and packet lengths are exponentially distributed. The proposed algorithm is both accurate and fast, allowing one to use the procedure to dimension optical buffers in next-generation optical packet switching systems

Performance issues in optical burst/packet switching

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-01524-3_8This chapter summarises the activities on optical packet switching (OPS) and optical burst switching (OBS) carried out by the COST 291 partners in the last 4 years. It consists of an introduction, five sections with contributions on five different specific topics, and a final section dedicated to the conclusions. Each section contains an introductive state-of-the-art description of the specific topic and at least one contribution on that topic. The conclusions give some points on the current situation of the OPS/OBS paradigms

GMPLS-OBS interoperability and routing acalability in internet

The popularization of Internet has turned the telecom world upside down over the last two decades. Network operators, vendors and service providers are being challenged to adapt themselves to Internet requirements in a way to properly serve the huge number of demanding users (residential and business). The Internet (data-oriented network) is supported by an IP packet-switched architecture on top of a circuit-switched, optical-based architecture (voice-oriented network), which results in a complex and rather costly infrastructure to the transport of IP traffic (the dominant traffic nowadays). In such a way, a simple and IP-adapted network architecture is desired. From the transport network perspective, both Generalized Multi-Protocol Label Switching (GMPLS) and Optical Burst Switching (OBS) technologies are part of the set of solutions to progress towards an IP-over-WDM architecture, providing intelligence in the control and management of resources (i.e. GMPLS) as well as a good network resource access and usage (i.e. OBS). The GMPLS framework is the key enabler to orchestrate a unified optical network control and thus reduce network operational expenses (OPEX), while increasing operator's revenues. Simultaneously, the OBS technology is one of the well positioned switching technologies to realize the envisioned IP-over-WDM network architecture, leveraging on the statistical multiplexing of data plane resources to enable sub-wavelength in optical networks. Despite of the GMPLS principle of unified control, little effort has been put on extending it to incorporate the OBS technology and many open questions still remain. From the IP network perspective, the Internet is facing scalability issues as enormous quantities of service instances and devices must be managed. Nowadays, it is believed that the current Internet features and mechanisms cannot cope with the size and dynamics of the Future Internet. Compact Routing is one of the main breakthrough paradigms on the design of a routing system scalable with the Future Internet requirements. It intends to address the fundamental limits of current stretch-1 shortest-path routing in terms of RT scalability (aiming at sub-linear growth). Although "static" compact routing works fine, scaling logarithmically on the number of nodes even in scale-free graphs such as Internet, it does not handle dynamic graphs. Moreover, as multimedia content/services proliferate, the multicast is again under the spotlight as bandwidth efficiency and low RT sizes are desired. However, it makes the problem even worse as more routing entries should be maintained. In a nutshell, the main objective of this thesis in to contribute with fully detailed solutions dealing both with i) GMPLS-OBS control interoperability (Part I), fostering unified control over multiple switching domains and reduce redundancy in IP transport. The proposed solution overcomes every interoperability technology-specific issue as well as it offers (absolute) QoS guarantees overcoming OBS performance issues by making use of the GMPLS traffic-engineering (TE) features. Keys extensions to the GMPLS protocol standards are equally approached; and ii) new compact routing scheme for multicast scenarios, in order to overcome the Future Internet inter-domain routing system scalability problem (Part II). In such a way, the first known name-independent (i.e. topology unaware) compact multicast routing algorithm is proposed. On the other hand, the AnyTraffic Labeled concept is also introduced saving on forwarding entries by sharing a single forwarding entry to unicast and multicast traffic type. Exhaustive simulation campaigns are run in both cases in order to assess the reliability and feasible of the proposals