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Covariance of the Queue Process Fed by Isonormal Gaussian Input Process
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class="card"> <div class="card-body"><strong>Paper Count:</strong> 87358</div> </div> </div> </div> <div class="card publication-listing mt-3 mb-3"> <h5 class="card-header" style="font-size:.9rem">Covariance of the Queue Process Fed by Isonormal Gaussian Input Process</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Samaneh%20Rahimirshnani">Samaneh Rahimirshnani</a>, <a href="https://publications.waset.org/abstracts/search?q=Hossein%20Jafari"> Hossein Jafari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we consider fluid queueing processes fed by an isonormal Gaussian process. We study the correlation structure of the queueing process and the rate of convergence of the running supremum in the queueing process. The Malliavin calculus techniques are applied to obtain relations that show the workload process inherits the dependence properties of the input process. As examples, we consider two isonormal Gaussian processes, the sub-fractional Brownian motion (SFBM) and the fractional Brownian motion (FBM). For these examples, we obtain upper bounds for the covariance function of the queueing process and its rate of convergence to zero. We also discover that the rate of convergence of the queueing process is related to the structure of the covariance function of the input process. <iframe src="https://publications.waset.org/abstracts/182769.pdf" style="width:100%; height:400px;" frameborder="0"></iframe> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=queue%20length%20process" title="queue length process">queue length process</a>, <a href="https://publications.waset.org/abstracts/search?q=Malliavin%20calculus" title=" Malliavin calculus"> Malliavin calculus</a>, <a href="https://publications.waset.org/abstracts/search?q=covariance%20function" title=" covariance function"> covariance function</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20Brownian%20motion" title=" fractional Brownian motion"> fractional Brownian motion</a>, <a href="https://publications.waset.org/abstracts/search?q=sub-fractional%20Brownian%20motion" title=" sub-fractional Brownian motion"> sub-fractional Brownian motion</a> </p> <a href="https://publications.waset.org/abstracts/182769/covariance-of-the-queue-process-fed-by-isonormal-gaussian-input-process" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/182769.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">63</span> </span> </div> </div> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/WASET-16th-foundational-anniversary.pdf">WASET 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