WAITING TIME OF M/D1,∞/1 QUEUE

2007 ◽  
Vol 24 (03) ◽  
pp. 383-399
Author(s):  
WOOJIN CHANG
Keyword(s):  
Steady State ◽  
Waiting Time ◽  
Service Time ◽  
Single Server ◽  
Poisson Arrival ◽  
Mean And Variance ◽  
Simulation Results ◽  
Set Up ◽  
The Individual ◽  
Individual Service

In this paper, we consider a single-server infinite capacity queue with Poisson arrival. The server takes all waiting customers as a batch into service, and the service time of the kth customer in a batch is a + b × k, where a and b are the set-up time and the individual service time for each customer, respectively. The steady-state mean and variance of waiting time of an arbitrary customer are obtained. Simulation results confirm our analysis.

scholarly journals Analysis of an MAP/PH/1 Queue with Flexible Group Service

2017 ◽  
Vol 27 (1) ◽  
pp. 119-131 ◽  
Author(s):  
Arianna Brugno ◽  
Ciro D’Apice ◽  
Alexander Dudin ◽  
Rosanna Manzo
Keyword(s):  
Markov Chain ◽  
Service Time ◽  
Arrival Process ◽  
Service Discipline ◽  
Single Server ◽  
Phase Type Distribution ◽  
Stationary Probability Distribution ◽  
The Individual ◽  
Number Of Customers ◽  
Individual Service

Abstract A novel customer batch service discipline for a single server queue is introduced and analyzed. Service to customers is offered in batches of a certain size. If the number of customers in the system at the service completion moment is less than this size, the server does not start the next service until the number of customers in the system reaches this size or a random limitation of the idle time of the server expires, whichever occurs first. Customers arrive according to a Markovian arrival process. An individual customer’s service time has a phase-type distribution. The service time of a batch is defined as the maximum of the individual service times of the customers which form the batch. The dynamics of such a system are described by a multi-dimensional Markov chain. An ergodicity condition for this Markov chain is derived, a stationary probability distribution of the states is computed, and formulas for the main performance measures of the system are provided. The Laplace–Stieltjes transform of the waiting time is obtained. Results are numerically illustrated.

Convexity results for single-server queues and for multiserver queues with constant service times

1990 ◽  
Vol 27 (02) ◽  
pp. 465-468 ◽  
Author(s):  
Arie Harel
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Sojourn Time ◽  
Interarrival Time ◽  
Service Rate ◽  
Single Server ◽  
Multiserver Queues ◽  
Service Rates ◽  
Constant Service Times ◽  
Number Of Customers

We show that the waiting time in queue and the sojourn time of every customer in the G/G/1 and G/D/c queue are jointly convex in mean interarrival time and mean service time, and also jointly convex in mean interarrival time and service rate. Counterexamples show that this need not be the case, for the GI/GI/c queue or for the D/GI/c queue, for c ≧ 2. Also, we show that the average number of customers in the M/D/c queue is jointly convex in arrival and service rates. These results are surprising in light of the negative result for the GI/GI/2 queue (Weber (1983)).

On a property of a refusals stream

1997 ◽  
Vol 34 (03) ◽  
pp. 800-805 ◽  
Author(s):  
Vyacheslav M. Abramov
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Busy Period ◽  
Elementary Proof ◽  
Queueing System ◽  
Queueing Systems ◽  
Single Server ◽  
Wide Family

This paper consists of two parts. The first part provides a more elementary proof of the asymptotic theorem of the refusals stream for an M/GI/1/n queueing system discussed in Abramov (1991a). The central property of the refusals stream discussed in the second part of this paper is that, if the expectations of interarrival and service time of an M/GI/1/n queueing system are equal to each other, then the expectation of the number of refusals during a busy period is equal to 1. This property is extended for a wide family of single-server queueing systems with refusals including, for example, queueing systems with bounded waiting time.

The general bulk queue as a matrix factorisation problem of the Wiener-Hopf type. Part II.

1975 ◽  
Vol 7 (3) ◽  
pp. 647-655 ◽  
Author(s):  
John Dagsvik
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Time Distribution ◽  
Single Server ◽  
Service Time Distribution ◽  
Time Process ◽  
Waiting Time Process ◽  
Bulk Queue ◽  
Erlang Distributions ◽  
Matrix Factorisation

In a previous paper (Dagsvik (1975)) the waiting time process of the single server bulk queue is considered and a corresponding waiting time equation is established. In this paper the waiting time equation is solved when the inter-arrival or service time distribution is a linear combination of Erlang distributions. The analysis is essentially based on algebraic arguments.

Convexity results for single-server queues and for multiserver queues with constant service times

1990 ◽  
Vol 27 (2) ◽  
pp. 465-468 ◽  
Author(s):  
Arie Harel
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Sojourn Time ◽  
Interarrival Time ◽  
Service Rate ◽  
Single Server ◽  
Multiserver Queues ◽  
Service Rates ◽  
Constant Service Times ◽  
Number Of Customers

We show that the waiting time in queue and the sojourn time of every customer in the G/G/1 and G/D/c queue are jointly convex in mean interarrival time and mean service time, and also jointly convex in mean interarrival time and service rate. Counterexamples show that this need not be the case, for the GI/GI/c queue or for the D/GI/c queue, for c ≧ 2. Also, we show that the average number of customers in the M/D/c queue is jointly convex in arrival and service rates.These results are surprising in light of the negative result for the GI/GI/2 queue (Weber (1983)).

A queue with Markov-dependent service times

1968 ◽  
Vol 5 (02) ◽  
pp. 461-466
Author(s):  
Gerold Pestalozzi
Keyword(s):  
Steady State ◽  
Generating Function ◽  
Waiting Time ◽  
Service Time ◽  
Queueing System ◽  
Single Channel ◽  
Probability Generating Function ◽  
Average Waiting Time ◽  
Poisson Input ◽  
The Mean

A queueing system is considered where each item has a property associated with it, and where the service time interposed between two items depends on the properties of both of these items. The steady state of a single-channel queue of this type, with Poisson input, is investigated. It is shown how the probability generating function of the number of items waiting can be found. Easily applied approximations are given for the mean number of items waiting and for the average waiting time.

scholarly journals An M/G/1 queue with multiple types of feedback and gated vacations

1997 ◽  
Vol 34 (03) ◽  
pp. 773-784 ◽  
Author(s):  
Onno J. Boxma ◽  
Uri Yechiali
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Queue Length ◽  
Time Distribution ◽  
Single Server ◽  
Service Time Distribution ◽  
Waiting Time Distribution ◽  
Single Server Queue ◽  
Server Queue ◽  
Poisson Arrivals

This paper considers a single-server queue with Poisson arrivals and multiple customer feedbacks. If the first service attempt of a newly arriving customer is not successful, he returns to the end of the queue for another service attempt, with a different service time distribution. He keeps trying in this manner (as an ‘old' customer) until his service is successful. The server operates according to the ‘gated vacation' strategy; when it returns from a vacation to find K (new and old) customers, it renders a single service attempt to each of them and takes another vacation, etc. We study the joint queue length process of new and old customers, as well as the waiting time distribution of customers. Some extensions are also discussed.

A note on stochastic decomposition in a GI/G/1 queue with vacations or set-up times

1985 ◽  
Vol 22 (02) ◽  
pp. 419-428 ◽  
Author(s):  
Bharat T. Doshi
Keyword(s):  
Steady State ◽  
Waiting Time ◽  
Sample Path ◽  
The Other ◽  
Independent Random Variables ◽  
Recurrence Time ◽  
Stochastic Decomposition ◽  
Set Up ◽  
Forward Recurrence Time ◽  
Main Model

In this note we prove some stochastic decomposition results for variations of theGI/G/1 queue. Our main model is aGI/G/1 queue in which the server, when it becomes idle, goes on a vacation for a random length of time. On return from vacation, if it finds customers waiting, then it starts serving the first customer in the queue. Otherwise it takes another vacation and so on. Under fairly general conditions the waiting time of an arbitrary customer, in steady state, is distributed as the sum of two independent random variables: one corresponding to the waiting time without vacations and the other to the stationary forward recurrence time of the vacation. This extends the decomposition result of Gelenbe and Iasnogorodski [5]. We use sample path arguments, which are also used to prove stochastic decomposition in aGI/G/1 queue with set-up time.

Cerebral and gaze data fusion for wheelchair navigation enhancement: case of distracted users

Robotica ◽  
2018 ◽  
Vol 37 (2) ◽  
pp. 246-263 ◽  
Author(s):  
Hachem A. Lamti ◽  
Mohamed Moncef Ben Khelifa ◽  
Vincent Hugel
Keyword(s):  
Neural Network ◽  
Steady State ◽  
Brain Regions ◽  
Experimental Protocol ◽  
Powered Wheelchair ◽  
Set Up ◽  
Individual Use ◽  
The Individual ◽  
New Framework ◽  
Better Than

SUMMARYThe goal of this paper is to present a new hybrid system based on the fusion of gaze data and Steady State Visual Evoked Potentials (SSVEP) not only to command a powered wheelchair, but also to account for users distraction levels (concentrated or distracted). For this purpose, a multi-layer perception neural network was set up in order to combine relevant gazing and blinking features from gaze sequence and brainwave features from occipital and parietal brain regions. The motivation behind this work is the shortages raised from the individual use of gaze-based and SSVEP-based wheelchair command techniques. The proposed framework is based on three main modules: a gaze module to select command and activate the flashing stimuli. An SSVEP module to validate the selected command. In parallel, a distraction level module estimates the intention of the user by mean of behavioral entropy and validates/inhibits the command accordingly. An experimental protocol was set up and the prototype was tested on five paraplegic subjects and compared with standard SSVEP and gaze-based systems. The results showed that the new framework performed better than conventional gaze-based and SSVEP-based systems. Navigation performance was assessed based on navigation time and obstacles collisions.

Queues with moving average service times

1967 ◽  
Vol 4 (03) ◽  
pp. 553-570 ◽  
Author(s):  
C. Pearce
Keyword(s):  
Service Time ◽  
Moving Average ◽  
Length Distribution ◽  
Transient State ◽  
Single Server ◽  
Queue Length Distribution ◽  
Mean And Variance ◽  
Poisson Arrivals ◽  
The Mean ◽  
Service Times

A model for the service time structure in the single server queue is given embodying correlations between contiguous and near-contiguous service times. A number of results are derived in the case of Poisson arrivals both for equilibrium and the transient state. In particular, Kendall's (equilibrium) result P (a departure leaves the queue empty) = 1 — (mean service time)/(mean inter-arrival time) is found still to hold good. The effect of the correlation on the mean and variance of the equilibrium queue length distribution is examined in a simple case.

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