On a Two-Server Queue with Consultation in Random Environment

Analysis of an Infinite-Server Queue $$MAP_k|G_k|\infty $$ in Random Environment with k Markov Arrival Streams and Random Volume of Customers

Information Technologies and Mathematical Modelling. Queueing Theory and Applications - Communications in Computer and Information Science ◽

10.1007/978-3-319-97595-5_24 ◽

2018 ◽

pp. 305-320

Author(s):

K. Kerobyan ◽

R. Kerobyan ◽

K. Enakoutsa

Keyword(s):

Random Environment ◽

Infinite Server ◽

Server Queue ◽

Markov Arrival

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The M/M/∞ queue in a random environment

Journal of Applied Probability ◽

10.2307/3214126 ◽

1986 ◽

Vol 23 (1) ◽

pp. 175-184 ◽

Cited By ~ 48

Author(s):

C. A. O'Cinneide ◽

P. Purdue

Keyword(s):

Steady State ◽

Random Environment ◽

Steady State Distribution ◽

State Distribution ◽

State Behavior ◽

Factorial Moments ◽

Numerical Examples ◽

Server Queue ◽

Service Rates ◽

Steady State Behavior

The M/M/∞ queue in a random environment is an infinite-server queue where arrival and service rates are stochastic processes. Here we study the steady-state behavior of such a system. Explicit results are obtained for the factorial moments, the impossibility of a ‘matrix-Poisson' steady-state distribution is demonstrated and two numerical examples are presented.

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Transient analysis of impatient customers in an M/M/1 disasters queue in random environment

Engineering Computations ◽

10.1108/ec-06-2019-0274 ◽

2020 ◽

Vol 37 (6) ◽

pp. 1945-1965 ◽

Cited By ~ 1

Author(s):

Sherif I. Ammar ◽

Tao Jiang ◽

Qingqing Ye

Keyword(s):

Random Environment ◽

Transient Analysis ◽

Time Dependent ◽

Single Server ◽

Single Server Queue ◽

Content Type ◽

Numerical Examples ◽

Server Queue ◽

Impatient Customer ◽

Multi Phase

Purpose This paper aims to consider a single server queue with system disasters and impatience behavior are evident in our daily life. For this purpose, authors require to know the general behavior of these systems. Transient analysis shows for us how the system will operate up to some time instant t. Design/methodology/approach In this paper, authors consider a single server queue with system disaster and impatient behavior of customers in a multi-phase random environment, in which the system transits to a repair state after each system disaster. When the system is in a failure phase or going through a repair phase, the new arrivals would be impatient. In case the system is not repaired before the customer’s time expires, the customer would leave the queue and never return. Moreover, after repair, the system becomes ready for service in an operative phase with probability $q_{i} \ge 0.$. Using generating functions along with continued fractions and some properties of the confluent hypergeometric function, authors obtained on their own results. Findings Explicit expressions have been obtained for the time-dependent probabilities of the underlying queuing model. Also, time-dependent mean and variance of customers in the system are deduced. Research limitations/implications The system authors are dealing with is somewhat complicated, there are some performance measures that cannot be achieved, but some of them have been obtained, such as the expectation and variance of the number of customers in the system. Practical implications Based on the obtained results, some numerical examples are some numerical examples are presented to illustrate the effect of various parameters on the behavior of the proposed system. Social implications Authors’ studied transient analysis of a single server queue with system disaster and impatient customer system is suitable for behavior interpretation of many systems in our lives, such as telecommunication networks, inventory systems and impatient telephone switchboard customers, manufacturing system and service system. Originality/value To the best of the author’s/authors’ knowledge and according to the literature survey, in a multi-phase random environment, no previous published article is presented for transient analysis of a single server queue with system disaster and impatient customer behavior in a random environment.

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

Austrian Journal of Statistics ◽

10.17713/ajs.v34i2.403 ◽

2016 ◽

Vol 34 (2) ◽

Cited By ~ 8

Author(s):

A.N. Dudin ◽

A.V. Kazimirsky ◽

V.I. Klimenok ◽

L. Breuer ◽

U. Krieger

Keyword(s):

Random Environment ◽

Queueing Systems ◽

Arrival Process ◽

Single Server ◽

Service Time Distribution ◽

Finite Buffer ◽

Phase Type ◽

Server Queue ◽

Finite State ◽

Markovian Random Environment

Queueing systems with feedback are well suited for the description of message transmission and manufacturing processes where a repeated service is required. In the present paper we investigate a rather general single server queue with a Markovian Arrival Process (MAP), Phase-type (PH) service-time distribution, a finite buffer and feedback which operates in a random environment. A finite state Markovian random environment affects the parameters of the input and service processes and the feedback probability. The stationary distribution of the queue and of the sojourn times as well as the loss probability are calculated. Moreover, Little’s law is derived.

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The M/M /∞ queue in a random environment

Journal of Applied Probability ◽

10.1017/s0021900200106370 ◽

1986 ◽

Vol 23 (01) ◽

pp. 175-184

Author(s):

C. A. O'Cinneide ◽

P. Purdue

Keyword(s):

Steady State ◽

Random Environment ◽

Steady State Distribution ◽

State Distribution ◽

State Behavior ◽

Factorial Moments ◽

Numerical Examples ◽

Server Queue ◽

Service Rates ◽

Steady State Behavior

The M/M/∞ queue in a random environment is an infinite-server queue where arrival and service rates are stochastic processes. Here we study the steady-state behavior of such a system. Explicit results are obtained for the factorial moments, the impossibility of a ‘matrix-Poisson' steady-state distribution is demonstrated and two numerical examples are presented.

Download Full-text