Mathematical Analysis of Queue with Phase Service: An Overview

We discuss various aspects of phase service queueing models. A large number of models have been developed in the area of queueing theory incorporating the concept of phase service. These phase service queueing models have been investigated for resolving the congestion problems of many day-to-day as well as industrial scenarios. In this survey paper, an attempt has been made to review the work done by the prominent researchers on the phase service queues and their applications in several realistic queueing situations. The methodology used by several researchers for solving various phase service queueing models has also been described. We have classified the related literature based on modeling and methodological concepts. The main objective of present paper is to provide relevant information to the system analysts, managers, and industry people who are interested in using queueing theory to model congestion problems wherein the phase type services are prevalent.

• Publication year

  2014

• Venue

  Advances in Operations Research

• Publication date

  2014-12-10

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1155/2014/240926
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• The Queueing Model MAP|PH|1|N with Feedback Operating in a Markovian Random Environment

  2016cited by this paper
• Availability analysis for embedded system with N-version programming using fuzzy approach

  2015cited by this paper
• Unreliable server M/G/1 queue with multi-optional services and multi-optional vacations

  2013cited by this paper
• Multiple vacation policy for MX/Hk/1 queue with un-reliable server

  2013cited by this paper
• A batch arrival retrial queuing system for essential and optional services with server breakdown and Bernoulli vacation

  2012cited by this paper
• A single server queueing system with two phases of service subject to server breakdown and Bernoulli vacation

  2012cited by this paper
• A Batch Arrival Retrial Queue with Two Phases of Service, Feedback and K Optional Vacations

  2012cited by this paper
• • OPTIMAL STRATEGY ANALYSIS OF AN N-POLICY TWO-PHASE MX/EK/1 GATED QUEUEING SYSTEM WITH SERVER STARTUP AND BREAK DOWNS

  2012cited by this paper
• Unreliable M^X/(G1,G2)/1 Retrial Queue with Bernoulli Feedback Under Modified Vacation Policy

  2012cited by this paper
• Maximum Entropy Approach for UnReliable Server Vacation Queueing Model with Optional Bulk Service

  2012cited by this paper
• Stationary analysis of a discrete-time GI/D-MSP/1 queue with multiple vacations

  2012cited by this paper
• Optimal control of (N, F) policy for unreliable server queue with multi-optional phase repair and start-up

  2012cited by this paper
• Busy period analysis of the level dependent PH/PH/1/K queue

  2011cited by this paper
• Discrete-time Geo1, GeoX2/G1, G2/1 retrial queue with two classes of customers and feedback

  2011cited by this paper
• The optimal control of an Mx/G/1 unreliable server queue with two phases of service and Bernoulli vacation schedule

  2011cited by this paper
• An M/Ek/1 queueing system with no damage service interruptions

  2011cited by this paper
• Analysis of a batch arrival general bulk service queueing system with variant threshold policy for secondary jobs

  2011cited by this paper
• Analysis of the finite source MAP/PH/N retrial G-queue operating in a random environment

  2011cited by this paper
• Queueing model with state-dependent bulk arrival and second optional service

  2011cited by this paper
• Economic application in a finite capacity multi-channel queue with second optional channel

  2011cited by this paper
• Bi-level threshold policy of M X /( G 1 , G 2 )/1 queue with early setup and single vacation

  2011cited by this paper
• SINGLE SERVER RETRIAL QUEUES WITH SECOND OPTIONAL SERVICE UNDER ERLANG SERVICES

  2011cited by this paper
• Optimal strategy analysis of an N-policy two-phase MX/M/1 queueing system with server startup and breakdowns

  2011cited by this paper
• Comparison of two randomized policy M/G/1 queues with second optional service, server breakdown and startup

  2010cited by this paper
• A batch arrival retrial queueing system with two phases of service and service interruption

  2010cited by this paper
• The discrete-time MAP/PH/1 queue with multiple working vacations

  2010cited by this paper
• Testability Estimation Framework

  2010cited by this paper
• An M X /G/1 retrial queue with two-phase service subject to active server breakdowns and two types of repair

  2010cited by this paper
• A discrete-time Geo X /G/1 retrial queueing system with starting failures and optional service

  2010cited by this paper
• The approximation analysis of the discrete-time Geo/Geo/1 system with additional optional service

  2010cited by this paper
• Optimal repairable Mx/G/1 queue with multi-optional services and Bernoulli vacation

  2010cited by this paper
• Computing packet loss probabilities of D-BMAP/PH/1/N queues with group services

  2010cited by this paper
• N-Policy for State-Dependent Batch Arrival Queueing System with l-Stage Service and Modified Bernoulli Schedule Vacation

  2010cited by this paper
• Analysis of the M[X]/G/1 queues with second multi-optional service and unreliable server

  2010cited by this paper
• Investigation of the BMAP/G/1→·/PH/1/M tandem queue with retrials and losses

  2010cited by this paper
• M/G/M QUEUE WITH TWO STAGE HETEROGENEOUS SERVICE COMPULSORY SERVER VACATION AND RANDOM BREAKDOWNS

  2010cited by this paper
• Analysis of a batch retrial queue with Bernoulli vacation and starting failures

  2010cited by this paper
• A Single Server M/G/1 Feedback Queue with Two Types of Service Having General Distribution

  2010cited by this paper
• A Two Phase Service M/G/1 Vacation Queue With General Retrial Times and Non-persistent Customers

  2010cited by this paper
• M/M/1 Retrial Queueing System with Two Types of Vacation Policies under Erlang - K Type Service

  2010cited by this paper
• M/M/1 Retrial Queueing System with Vacation Interruptions Under Erlang-K Service

  2010cited by this paper
• A queueing system with n-phases of service and (n-1)-types of retrial customers

  2010cited by this paper
• Analysis of a two-phase queueing system with a fixed-size batch policy

  2010cited by this paper
• Threshold N-Policy for MX/H2/1 Queueing System with Un-reliable Server and Vacations

  2010cited by this paper
• A repairable queueing model with two-phase service, start-up times and retrial customers

  2010cited by this paper
• On the multi-phase M/G/1 queueing system with random feedback

  2009cited by this paper
• M[X]/(G1, G2)/1 RETRIAL QUEUE UNDER BERNOULLI VACATION SCHEDULES WITH GENERAL REPEATED ATTEMPTS AND STARTING FAILURES

  2009cited by this paper
• An MX/G/1 unreliable retrial queue with two phases of service and Bernoulli admission mechanism

  2009cited by this paper
• A Note on M/G/1 Queue with Two Phases of Service and Linear Repeated Attempts Subject to Random Breakdown

  2009cited by this paper
• A single server retrial queue with general retrial times and two-phase service

  2009cited by this paper
• An M/G/1 Retrial Queue with an Additional Phase of Second Service and Gerneral Retrial Times

  2009cited by this paper
• Performance Analysis of an M/G/1 Retrial Queue with Non-Persistent Calls, Two Phases of Heterogeneous Service and Different Vacation Policies

  2009cited by this paper
• The well-posedness of an M/G/1 queue with second optional service and server breakdown

  2009cited by this paper
• A Note on Maximum Entropy in Queueing Problems

  2009cited by this paper
• The MAP/PH/1/N queue with flows of customers as a model for traffic control in telecommunication networks

  2009cited by this paper
• A two-phase queueing system with repeated attempts and Bernoulli vacation schedule

  2009cited by this paper
• A Two Phase M/G/1 Feedback Queue with Multiple Server Vacation

  2009cited by this paper
• Two-phase queuing system with a threshold strategy of retrial calls

  2009cited by this paper
• Notes of M/G/1 system under the $${\langle p, T \rangle}$$ policy with second optional service

  2009cited by this paper
• An Mx/(G1,G2)/1/G(BS)/Vs with Optional Second Service and Admissibility Restricted

  2009cited by this paper
• An M/G/1 queue with two phases of service subject to the server breakdown and delayed repair

  2009cited by this paper
• On the BMAP/G/1 G-queues with second optional service and multiple vacations

  2009cited by this paper
• The N-policy for an unreliable server with delaying repair and two phases of service

  2009cited by this paper
• A Vacation Queue with Additional Optional Service in Batches

  2009cited by this paper
• The MAP/(PH/PH)/1 queue with self-generation of priorities and non-preemptive service

  2009cited by this paper
• An M/G/1 retrial G-queue with preemptive resume and feedback under N-policy subject to the server breakdowns and repairs

  2009cited by this paper
• An M/G/1 retrial queueing system with two phases of service subject to the server breakdown and repair

  2008cited by this paper
• Optimization on bicriterion policies for M/G/1 system with second optional service

  2008cited by this paper
• The BMAP/PH/N retrial queue with Markovian flow of breakdowns

  2008cited by this paper
• The M/M/1 Queue with Single Working Vacation

  2008cited by this paper
• Analysis of a retrial queue with two-phase service and server vacations

  2008cited by this paper
• A Hysteretic Bulk Quorum Queue with a Choice of Service and Optional Re-Service

  2008cited by this paper
• A TWO PHASE QUEUE SYSTEM WITH BERNOULLI FEEDBACK AND BERNOULLI SCHEDULE SERVER VACATION

  2008cited by this paper
• Steady state analysis of a M x /G/1 queue with two service modes and multiple vacations

  2008cited by this paper
• On the Single Server Batch Arrival Retrial Queue with General Vacation Time under Bernoulli Schedule and Two phases of Heterogeneous Service

  2008cited by this paper
• Steady state analysis of an M/G/1 queue with linear retrial policy and two phase service under Bernoulli vacation schedule

  2008cited by this paper
• An M[x]/G/1 system with startup server and J additional options for service

  2008cited by this paper
• A batch arrival Bernoulli vacation queue with a random setup time under restricted admissibility policy

  2007cited by this paper
• A two phase batch arrival retrial queueing system with Bernoulli vacation schedule

  2007cited by this paper
• A discrete-time Geo/G/1 retrial queue with starting failures and second optional service

  2007cited by this paper
• A Repairable M/G/1 Retrial Queue with Bernoulli Vacation and Two-Phase Service

  2007cited by this paper
• M/Ek/1 Queueing System with Working Vacation

  2007cited by this paper
• Sojourn time analysis of a queueing system with two‐phase service and server vacations

  2007cited by this paper
• The BMAP/G/1 -> ./PH/1/M tandem queue with feedback and losses

  2007cited by this paper
• A Bulk Service Queue with a Choice of Service and Re-Service under Bernoulli Schedule

  2007cited by this paper
• The processor-sharing queue with bulk arrivals and phase-type services

  2007cited by this paper
• Steady state analysis of an Mx/G/1 queue with two phase service and Bernoulli vacation schedule under multiple vacation policy

  2007cited by this paper
• How many servers are best in a dual-priority M/PH/k system?

  2006cited by this paper
• A matrix-analytic solution for the DBMAP/PH/1 priority queue

  2006cited by this paper
• Steady state analysis of an Mx/(G1,G2)/1 queue with restricted admissibility and random setup time

  2006influential reference
• The transient solution to M/Ek/1 queue

  2006cited by this paper
• AN M2/G2/1 RETRIAL QUEUE WITH PRIORITY CUSTOMERS, 2 ND OPTIONAL SERVICE AND LINEAR RETRIAL POLICY

  2006cited by this paper
• Two-Phase Queueing System with a Markov Arrival Process and Blocking

  2006cited by this paper
• Geo/G/1 retrial queue with 2nd optional service

  2006cited by this paper
• Characterizing output processes of Em/Ek/1 queues

  2006cited by this paper
• An M/G/1 retrial queue with second multi-optional service, feedback and unreliable server

  2006cited by this paper
• A Batch Arrival Queue with a Second Optional Service Channel Under N-Policy

  2006influential reference
• A two phases queueing system with Bernoulli vacation schedule under multiple vacation policy

  2006influential reference
• The Generally Weighted Moving Average Median Control Chart

  2006cited by this paper
• A Single Server Queue with Two Phases of Heterogeneous Service under Bernoulli Schedule and a General Vacation Time

  2005cited by this paper

• Comparative analysis of M/G/K queueing model with artificial neural networks for service system dynamics

  2025cites this paper
• Optimal control of a two-phase heterogeneous service retrial queueing system with collisions and delayed vacations

  2024cites this paper
• Optimal management strategies of renewable energy systems with hyperexponential service provisioning: an economic investigation

  2023cites this paper
• Fuzzy Inventory Model with Eco Friendly Package, Carbon Emission, Cap Policy and Life Cycle Assessment Technology

  2023cites this paper
• EDUCAÇÃO FINANCEIRA TRANSFORMATIVA SOBRE O CONSUMO SUSTENTÁVEL DO MICROCRÉDITO POR IDOSOS EM SITUAÇÕES DE VULNERABILIDADES QUE SE ENTRELAÇAM

  2022cites this paper
• Transient analysis and ANFIS computing of unreliable single server queueing model with multiple stage service and functioning vacation

  2022cites this paper
• EXPLORING THE IMPACT OF BURSTINESS ON THE SERVICE PROCESS AT THE CASH REGISTER

  2021influential citation
• Reliability and Sensitivity Analysis of Retrial Queue with Optional k-Phases Services, Vacation and Feedback

  2021cites this paper
• Cost Analysis of M/M/1/N queue with working breakdowns and a two-phase services

  2021cites this paper
• A queue theory in the cross-polarization of antenna in satellite communication

  2021cites this paper
• PREEMPTIVE-RESUME PRIORITY QUEUE SYSTEM WITH ERLANG SERVICE DISTRIBUTION

  2021cites this paper
• Development of a model of the service system of batch arrivals in the passengers flow of public transport

  2019cites this paper
• Approximate controllability of stochastic bounds of stationary distribution of an M/G/1 queue with repeated attempts and two-phase service

  2018cites this paper
• BUSINESS ENVIRONMENTS UNDER SUB-QUEUED PREFERENCES

  2018cites this paper
• Predictor Analysis on Non-parametric Bulk Arrival Fuzzy Queuing System

  2017cites this paper
• Queueing systems with correlated arrival flows and their applications to modeling telecommunication networks

  2017cites this paper