{"product_id":"the-analysis-of-the-time-dependent-behavior-of-queues-von-rieske-hadianti","title":"The analysis of the time-dependent behavior of queues","description":"\u003cp\u003eThis book studies the time-dependent behavior of queuing systems which has non-empty initial work load. The technique  used to analyze the behavior of the queueing systems studied in this book is based on the Wiener-Hopf factorization. The first major step in the analysis is the  derivation of  the (system of) transformed Wiener-Hopf equation(s).  Wiener-Hopf factorization is then applied to its symbol. Since the queueing systems we consider have a non-zero initial working load,  the Wiener-Hopf factorization should be followed by a decomposition on a certain (matrix) function. The  Wiener-Hopf factorization and the decomposition yields a (formal) solution of the (system of) equation(s).If the stability condition is fulfilled, then the steady-state distributions of interest can be determined by applying  Abel's limit theorem to the  solution of the (system of) equation(s).In this book it is shown how the time-dependent distributions converge to the steady-state distribution.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783844333275\"\u003e\u003ch3\u003ethe application of Wiener-Hopf techniques\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783844333275","offer_id":39495927922781,"sku":"9783844333275","price":79.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/8e2c46d4-d056-4719-87b6-16155505ab88.jpg?v=1768893793","url":"https:\/\/shop.autorenwelt.de\/products\/the-analysis-of-the-time-dependent-behavior-of-queues-von-rieske-hadianti","provider":"Autorenwelt Shop","version":"1.0","type":"link"}