Busy period analysis of the level dependent PH/PH/1/K queue

In this paper, we study the transient behavior of a level dependent single server queuing system with a waiting room of finite size during the busy period. The focus is on the level dependent PH/PH/1/K queue. We derive in closed form the joint transform of the length of the busy period, the number of customers served during the busy period, and the number of losses during the busy period. We differentiate between two types of losses: the overflow losses that are due to a full queue and the losses due to an admission controller. For the M/PH/1/K, M/PH/1/K under a threshold policy, and PH/M/1/K queues, we determine simple expressions for their joint transforms.

• Publication year

  2011

• Venue

  Queueing Syst. Theory Appl.

• Publication date

  2011-03-01

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1007/s11134-011-9213-6
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Busy period analysis of the state dependent M/M/1/K queue

  2010cited by this paper
• Transient analysis of the state dependent M/M/1/K queue

  2009cited by this paper
• A generalized Vandermonde determinant

  2003cited by this paper
• Losses per cycle in a single-server queue

  2002cited by this paper
• A note on losses in M/GI/1/n queues

  1999cited by this paper
• On a property of a refusals stream

  1997cited by this paper
• Modeling Vehicular Traffic Flow using M/G/C/C State Dependent Queueing Models

  1997cited by this paper
• On the Busy Period of an M/G/1/K Queue

  1994cited by this paper
• Transient and busy period analysis of theGI/G/1 queue: The method of stages

  1992cited by this paper
• M/G/1/N Queue with Vacation Time and Exhaustive Service Discipline

  1984cited by this paper
• Matrix-geometric solutions in stochastic models - an algorithmic approach

  1982cited by this paper
• The N/G/1 queue and its detailed analysis

  1980cited by this paper
• A Single Server

  1979cited by this paper
• The queue G/M/m/N: Busy period and cycle, waiting time under reverse and random order service

  1978influential reference
• Busy periods in time-dependent M / G /1 queues

  1976cited by this paper
• The Single Server Queue.

  1972cited by this paper
• Inverses of Vandermonde Matrices

  1964cited by this paper
• Introduction to the Theory of Queues.

  1963cited by this paper
• Introduction to the Theory of Queues

  1963cited by this paper

• Distribution of the number of losses in busy-periods of oscillating MX/G/1/(n, a, b) systems

  2021cites this paper
• Numbers of Served and Lost Customers in Busy-Periods of M/M/1/n Systems with Balking

  2020cites this paper
• On Time-to-Buffer Overflow Distribution in a single-Machine discrete-Time System with finite Capacity

  2020cites this paper
• Distribution of the time to buffer overflow in the M/G/1/N-type queueing model with batch arrivals and multiple vacation policy

  2019cites this paper
• Time to Start a Crowded Period in a Finite-Buffer Queue with Poisson Input Flow and General Processing Times

  2018cites this paper
• Moments of losses during busy-periods of regular and nonpreemptive oscillating $$M^X/G/1/n$$MX/G/1/n systems

  2017cites this paper
• Distribution of the time to buffer overflow in the single-server queueing model with multiple vacation policy

  2017cites this paper
• Moments of losses during busy-periods of regular and nonpreemptive oscillating MX/G/1/n systems

  2017cites this paper
• Distribution of time to buffer overflow in a finite-buffer manufacturing model with unreliable machine

  2017cites this paper
• A SURVEY ON QUEUES IN MACHINING SYSTEM: PROGRESS FROM 2010 TO 2017

  2017cites this paper
• A simple method to obtain the stochastic decomposition structure of the busy period in Geo/Geo/1/N vacation queue

  2015cites this paper
• Approximations for the waiting-time distribution in an $$M/PH/c$$M/PH/c priority queue

  2015cites this paper
• A simple method to obtain the stochastic decomposition structure of the busy period in Geo/Geo/1/N vacation queue

  2015cites this paper
• Mathematical Analysis of Queue with Phase Service: An Overview

  2014cites this paper
• On time to buffer saturation in a GI/M/1/N-type queue

  2012cites this paper
• On the distribution of the time to buffer overflow in a queueing system with a general-type input stream

  2012cites this paper
• The variance of departure processes: puzzling behavior and open problems

  2011cites this paper