In this article, we present a novel discrete-time Markov chain model of book-ahead bandwidthsharing mechanisms. We use this analytical model and a simulation model to understand the benefits of book-ahead (BA) bandwidth-sharing when compared to the immediate-request (IR) call-blocking mode of bandwidth-sharing in circuit-switched networks. We study two different BA schemes, BA-all, in which the caller accepts any set of available timeslots, and BA-n, in which the caller specifies n call-initiation time options. Numerical results show that the BA-all achieves 95% utilization with a call-blocking probability of only 1%, while in the IR mode, call blocking probability is 23% even when utilization is only 80%. The BA-n schemes perform as well as the BA-all scheme if the call-initiation time options are restricted to fall on timeslot boundaries separated by the minimum call holding time.The length of the advance-reservation horizon, K, is shown to increase linearly with call holding time, H. The ratio K/H is primarily dependent on the link capacity in channels. For example, if the link is divided into 10 channels, to achieve a 2% call blocking probability, the advance-reservation horizon needs to be a factor of 4 times the call holding time. In other words, the extra data storage and processing required to accept and maintain advance reservations is not significant.
Top-k retrieval over main-memory inverted indexes is at the core of many modern applications: from large scale web search and advertising platforms, to text extenders and content management systems. In these systems, queries are evaluated using two major families of algorithms: document-at-a-time (DAAT) and term-at-a-time (TAAT). DAAT and TAAT algorithms have been studied extensively in the research literature, but mostly in disk-based settings. In this paper, we present an analysis and comparison of several DAAT and TAAT algorithms used in Yahoo!'s production platform for online advertising. The low-latency requirements of online advertising systems mandate memory-resident indexes. We compare the performance of several query evaluation algorithms using two real-world ad selection datasets and query workloads. We show how some adaptations of the original algorithms for main memory setting have yielded significant performance improvement, reducing running time and cost of serving by 60% in some cases. In these results both the original and the adapted algorithms have been evaluated over memory-resident indexes, so the improvements are algorithmic and not due to the fact that the experiments used main memory indexes.
Abstract-Optical networks with book-ahead bandwidth schedulers are being deployed to meet the high-speed and predictable-service networking requirements of applications in the scientific research community. We present an analytical model for a single-link book-ahead bandwidth scheduler, which responds to advance reservation requests with the first-available time interval in which a channel is available. The link is assumed to be divided into m channels, and time is discretized into intervals. Our proposed model is a non-homogeneous continuous-time Markov chain, which has an embedded discrete-time Markov chain. We solve the model for call congestion, mean scheduling delay, and link utilization. This model can be used by network designers to select the size of the reservation window, K, in timeinterval units, corresponding to a desired set of values for the output metrics, for a given value of m. For example, when m is 8, increasing the reservation window beyond 4 intervals does not affect the call congestion or system utilization, but causes the mean scheduling delay to increase. We show with comparative simulations that our analytical model can be used as a solution for an M/D/m/p queueing system at moderate-to-high loads.
Abstract-Resource-sharing mechanisms can be classified into the broad categories of reservation systems and queueing systems. There are key differences between the two types of systems, and each has advantages and disadvantages. In this work, these differences are characterized, and a general reservation system model (GRSM) is proposed. Under four different sets of assumptions, the GRSM is reduced to analytically tractable models for which solutions are provided. In two cases, queueing model solutions are used, and in the remaining two cases, Discrete Time Markov Chain (DTMC) models are solved. A fifth model, defined through a different set of simplifying assumptions to the GRSM, is solved with simulations. Next, several examples of commonly encountered reservation and queueing systems are identified, and analyzed using one of these four simplified analytical models, or the fifth simulation model. The purpose of these analyses is to understand why certain systems belonging to the same category of examples use reservation systems while others use queueing systems. For example, while both physicians and bank tellers are human servers, the former use reservation systems while the latter use queueing systems.
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