{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/9637"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/9637","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"The Ph(t)/Ph(t)/s/c Queueing Model and Approximation","abstract":"Time-dependent queueing models are important since most of real-life problems are time-dependent. We develop a numerical approximation algorithm for the mean, variance and higher-order moments of the number of entities in the system at time t for the Ph(t)/Ph(t)/s/c queueing model. This model can be thought as a reparameterization to the G(t)/GI(t)/s. Our approach is to partition the state space into known and identifiable structures, such as the M(t)/M(t)/s/c or M(t)/M(t)/1 queueing models. We then use the Polya-Eggenberger distribution to approximate certain unknown probabilities via a two-moment matching algorithm. We describe the necessary steps to validate the approximation and measure the accuracy of the model.","abstract_html":"Time-dependent queueing models are important since most of real-life problems are time-dependent. We develop a numerical approximation algorithm for the mean, variance and higher-order moments of the number of entities in the system at time t for the Ph(t)/Ph(t)/s/c queueing model. This model can be thought as a reparameterization to the G(t)/GI(t)/s. Our approach is to partition the state space into known and identifiable structures, such as the M(t)/M(t)/s/c or M(t)/M(t)/1 queueing models. We then use the Polya-Eggenberger distribution to approximate certain unknown probabilities via a two-moment matching algorithm. We describe the necessary steps to validate the approximation and measure the accuracy of the model.","abstract_has_math":false,"creators":["Rueda, Javier Eduardo"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Industrial and Systems Engineering","degree_department":"Industrial and Systems Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":["Taaffe, Michael R."],"committee_members":["Castagliola, Philippe","Lin, Kyle Y."],"year":2003,"date_issued":"2003-12-05","date_published":"2003-12-05","updated_at":"2026-07-22T22:18:41Z","subjects":["Polya-Eggenberger","Queueing","phase-type","stochastic","time-dependent queues"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-12092003-164431"],"render_values":[{"text":"etd-12092003-164431","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/9637","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Taaffe, Michael R."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Castagliola, Philippe","Lin, Kyle Y."]},{"key":"dc:contributor.department","label":"Department","values":["Industrial and Systems Engineering"]},{"key":"dc:creator","label":"Author","values":["Rueda, Javier Eduardo"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2011-08-06T14:43:08Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2011-08-06T14:43:08Z","2003-12-16"]},{"key":"dc:date.issued","label":"Date","values":["2003-12-05"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Industrial and Systems Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Polya-Eggenberger","Queueing","phase-type","stochastic","time-dependent queues"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-12092003-164431"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/9637"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Time-dependent queueing models are important since most of real-life problems are time-dependent. We develop a numerical approximation algorithm for the mean, variance and higher-order moments of the number of entities in the system at time t for the Ph(t)/Ph(t)/s/c queueing model. This model can be thought as a reparameterization to the G(t)/GI(t)/s. Our approach is to partition the state space into known and identifiable structures, such as the M(t)/M(t)/s/c or M(t)/M(t)/1 queueing models. We then use the Polya-Eggenberger distribution to approximate certain unknown probabilities via a two-moment matching algorithm. We describe the necessary steps to validate the approximation and measure the accuracy of the model."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["The Ph(t)/Ph(t)/s/c Queueing Model and Approximation"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Taaffe, Michael R."],"dc:contributor.committeemember":["Castagliola, Philippe","Lin, Kyle Y."],"dc:contributor.department":["Industrial and Systems Engineering"],"dc:creator":["Rueda, Javier Eduardo"],"dc:date.accessioned":["2011-08-06T14:43:08Z"],"dc:date.available":["2011-08-06T14:43:08Z","2003-12-16"],"dc:date.issued":["2003-12-05"],"dc:description.abstract":["Time-dependent queueing models are important since most of real-life problems are time-dependent. We develop a numerical approximation algorithm for the mean, variance and higher-order moments of the number of entities in the system at time t for the Ph(t)/Ph(t)/s/c queueing model. This model can be thought as a reparameterization to the G(t)/GI(t)/s. Our approach is to partition the state space into known and identifiable structures, such as the M(t)/M(t)/s/c or M(t)/M(t)/1 queueing models. We then use the Polya-Eggenberger distribution to approximate certain unknown probabilities via a two-moment matching algorithm. We describe the necessary steps to validate the approximation and measure the accuracy of the model."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:identifier.other":["etd-12092003-164431"],"dc:identifier.uri":["http://hdl.handle.net/10919/9637"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Polya-Eggenberger","Queueing","phase-type","stochastic","time-dependent queues"],"dc:title":["The Ph(t)/Ph(t)/s/c Queueing Model and Approximation"],"dc:type":["Thesis"],"thesis:degree_discipline":["Industrial and Systems Engineering"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:18:41Z"}