scholarly journals Buffer Overflow Period in a MAP Queue

2007 ◽  
Vol 2007 ◽  
pp. 1-18 ◽  
Author(s):  
Andrzej Chydzinski
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
Markovian Arrival Process ◽  
Numerical Calculations ◽  
Buffer Overflow ◽  
Arrival Process ◽  
Service Time Distribution ◽  
Process Map ◽  
General Service ◽  
Number Of Cells

The buffer overflow period in a queue with Markovian arrival process (MAP) and general service time distribution is investigated. The results include distribution of the overflow period in transient and stationary regimes and the distribution of the number of cells lost during the overflow interval. All theorems are illustrated via numerical calculations.

The discrete-time single-server queue with time-inhomogeneous compound Poisson input and general service time distribution

1978 ◽  
Vol 15 (3) ◽  
pp. 590-601 ◽  
Author(s):  
Do Le Minh
Keyword(s):  
Discrete Time ◽  
Service Time ◽  
Time Distribution ◽  
Single Server ◽  
Service Time Distribution ◽  
Queueing Model ◽  
Compound Poisson ◽  
Poisson Input ◽  
Server Queue ◽  
General Service

This paper studies a discrete-time, single-server queueing model having a compound Poisson input with time-dependent parameters and a general service time distribution.All major transient characteristics of the system can be calculated very easily. For the queueing model with periodic arrival function, some explicit results are obtained.

The discrete-time single-server queue with time-inhomogeneous compound Poisson input and general service time distribution

1978 ◽  
Vol 15 (03) ◽  
pp. 590-601 ◽  
Author(s):  
Do Le Minh
Keyword(s):  
Discrete Time ◽  
Service Time ◽  
Time Distribution ◽  
Single Server ◽  
Service Time Distribution ◽  
Queueing Model ◽  
Compound Poisson ◽  
Poisson Input ◽  
Server Queue ◽  
General Service

This paper studies a discrete-time, single-server queueing model having a compound Poisson input with time-dependent parameters and a general service time distribution. All major transient characteristics of the system can be calculated very easily. For the queueing model with periodic arrival function, some explicit results are obtained.

Analysis of finite-capacity polling systems

1991 ◽  
Vol 23 (2) ◽  
pp. 373-387 ◽  
Author(s):  
Hideaki Takagi
Keyword(s):  
Time Distribution ◽  
Arrival Process ◽  
Polling Systems ◽  
Single Server ◽  
Service Time Distribution ◽  
Finite Capacity ◽  
Poisson Arrival ◽  
Finite Capacity Queues ◽  
General Service ◽  
Limited Service

We consider a system of N finite-capacity queues attended by a single server in cyclic order. For each visit by the server to a queue, the service is given continuously until that queue becomes empty (exhaustive service), given continuously only to those customers present at the visiting instant (gated service), or given to only a single customer (limited service). The server then switches to the next queue with a random switchover time, and administers the same type of service there similarly. For such a system where each queue has a Poisson arrival process, general service time distribution, and finite capacity, we find the distribution of the waiting time at each queue by utilizing the known results for a single M/G/1/K queue with multiple vacations.

scholarly journals An Analysis of a Close-Type Queuing System with General Service-Time Distribution

1970 ◽  
Vol 3 (1) ◽  
pp. 77-82
Author(s):  
Yoshio Yoshioka ◽  
Tomoyuki Nagase
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
Probability Distributions ◽  
Queuing System ◽  
Multiprocessor System ◽  
Service Time Distribution ◽  
Systems Model ◽  
Proposed Model ◽  
Repair Procedure ◽  
General Service

This paper presents an innovative approach to solve probability distributions of a close feed back loop type queuing system with general service time distribution. This model is applied to a multiprocessor system where some of its nodes are performed a repair procedure during a nodes malfunction condition. Our model is appropriate for a multiprocessor system that employs a common bus or for a multi-node system in computer networks. A meticulous analysis of the systems model has been conducted and numerical results have been obtained to scrutinize the proposed model.

Analysis of finite-capacity polling systems

1991 ◽  
Vol 23 (02) ◽  
pp. 373-387 ◽  
Author(s):  
Hideaki Takagi
Keyword(s):  
Time Distribution ◽  
Arrival Process ◽  
Polling Systems ◽  
Single Server ◽  
Service Time Distribution ◽  
Finite Capacity ◽  
Poisson Arrival ◽  
Finite Capacity Queues ◽  
General Service ◽  
Limited Service

We consider a system of N finite-capacity queues attended by a single server in cyclic order. For each visit by the server to a queue, the service is given continuously until that queue becomes empty (exhaustive service), given continuously only to those customers present at the visiting instant (gated service), or given to only a single customer (limited service). The server then switches to the next queue with a random switchover time, and administers the same type of service there similarly. For such a system where each queue has a Poisson arrival process, general service time distribution, and finite capacity, we find the distribution of the waiting time at each queue by utilizing the known results for a single M/G/1/K queue with multiple vacations.

Rate conservation for stationary processes

1991 ◽  
Vol 28 (1) ◽  
pp. 146-158 ◽  
Author(s):  
Josep M. Ferrandiz ◽  
Aurel A. Lazar
Keyword(s):  
Service Time ◽  
Conservation Law ◽  
Time Distribution ◽  
Distribution Density ◽  
Queueing System ◽  
Arrival Process ◽  
Stationary Processes ◽  
Service Time Distribution ◽  
Stochastic Intensity ◽  
Residual Service

We derive a rate conservation law for distribution densities which extends a result of Brill and Posner. Based on this conservation law, we obtain a generalized Takács equation for the G/G/m/B queueing system that only requires the existence of a stochastic intensity for the arrival process and the residual service time distribution density for the G/GI/1/B queue. Finally, we solve Takács' equation for the N/GI/1/∞ queueing system.

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