{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T09:10:11Z","timestamp":1698225011101},"reference-count":23,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,9,1]],"date-time":"2006-09-01T00:00:00Z","timestamp":1157068800000},"content-version":"vor","delay-in-days":4657,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Appl. Stochastic Models Data Anal."],"published-print":{"date-parts":[[1993,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In classical studies of loss systems with restricted availability, the utilization was suggested of a probabilistic loss function, defining the conditional probability of an incoming call being rejected, as a function of the number of occupations in the destination group of servers. This paper gives an exact analysis of stochastic processes of practical relevance, associated with a system with MMPP (Markov Modulated Poisson Process) input, finite queueing capacity and a general loss function, assuming exponential service times. In addition to the process defining the state of the system at any instant, the analysis of the overflow point process (associated with the rejected arriving customers), the accepted point process (associated with the accepted arriving customers), and of the departure process will be presented. Together with the exact analysis of this system, based on the matrix analytical methodology of Neuts, (1981), we will derive expressions for calculating some key\u2010parameters of pertinent associated processes, which may also be used for their approximate modelling. Also, examples of applications and of blocking probability calculations in specific models of this class will be presented.<\/jats:p>","DOI":"10.1002\/asm.3150090402","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T01:15:39Z","timestamp":1180401339000},"page":"279-299","source":"Crossref","is-referenced-by-count":0,"title":["A stochastic system with MMPP input and an access function"],"prefix":"10.1002","volume":"9","author":[{"given":"Lino","family":"Tralh\u00e3o","sequence":"first","affiliation":[]},{"given":"Jos\u00e9","family":"Craveirinha","sequence":"additional","affiliation":[]},{"given":"Jos\u00e9","family":"Paix\u00e3o","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,9]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"B.Wallstrom \u2018Congestion studies in telephone systems with overflow facilities\u2019 Ericsson Technics No. 3 1966 pp.190\u2013351."},{"issue":"3","key":"e_1_2_1_3_2","first-page":"267","article-title":"Adaptive traffic routing in telephone networks","volume":"8","author":"Bel G.","year":"1985","journal-title":"Large Scale Systems Journal"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","unstructured":"H.Heffes \u2018A class of data traffic processes\u2014covariance function characterization and related queueing results\u2019 Bell. Syst. Tech. J. No. 59 897\u2013929(1980).","DOI":"10.1002\/j.1538-7305.1980.tb03039.x"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/JSAC.1986.1146393"},{"key":"e_1_2_1_6_2","unstructured":"J. M.Holtzman \u2018Chacteristics of superpositions of traffic streams\u2019 Brussels Specialist seminar on ISDN Traffic Issues Brussels 1986."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/26.20117"},{"issue":"2","key":"e_1_2_1_8_2","article-title":"A multi\u2010class multi\u2010commodity flow model of a fast packet switched network","volume":"23","author":"Rossiter M. H.","year":"1989","journal-title":"A. T. R."},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","unstructured":"A.Kuczura \u2018The interrupted Poisson process as an overflow process\u2019 Bell. Syst. Tech. Jour. No. 52 187\u2013194(1973).","DOI":"10.1002\/j.1538-7305.1973.tb01971.x"},{"key":"e_1_2_1_10_2","volume-title":"Structured Stochastic Matrices of M\/G\/1 Type and Their Applications","author":"Neuts M. F.","year":"1989"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1080\/15326349108807174"},{"key":"e_1_2_1_12_2","volume-title":"Proc. Int. Teletraffic Congress","author":"Neuts M. F.","year":"1991"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.2307\/3213143"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.2307\/1426330"},{"key":"e_1_2_1_15_2","volume-title":"5th Int. Symp. Appl. Stock. Models and Data Analysis","author":"Tralh\u00e3o L. M.","year":"1991"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCOM.1985.1096202"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1973.tb02036.x"},{"key":"e_1_2_1_18_2","volume-title":"Matrix\u2010Geometric Solutions in Stochastic Models","author":"Neuts M. F.","year":"1981"},{"key":"e_1_2_1_19_2","unstructured":"K. S.Meier \u2018A statistical procedure for fitting Markov\u2010modulated Poisson processes\u2019 Ph. D. Dissertation University of Delaware 1984."},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.2307\/1426036"},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-5592-3"},{"key":"e_1_2_1_22_2","volume-title":"Introduction to Queueing Theory","author":"Cooper R.","year":"1981"},{"issue":"6","key":"e_1_2_1_23_2","first-page":"472","article-title":"More accurate calculations of overflow traffic from crossbar group selectors","volume":"13","author":"Smith N. M. 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