scholarly journals Analysis of the State-Dependent Queueing Model and Its Application to Battery Swapping and Charging Stations

2020 ◽  
Vol 12 (6) ◽  
pp. 2343
Author(s):  
Doo Il Choi ◽  
Dae-Eun Lim
Keyword(s):  
Congestion Control ◽  
Queue Length ◽  
Blocking Probability ◽  
Control Policy ◽  
Embedded Markov Chain ◽  
Queueing Model ◽  
Leaky Bucket ◽  
Numerical Examples ◽  
Charging Station ◽  
Mean Waiting Time

This study analyzes the performance of a queue length-dependent overload control policy using a leaky bucket (LB) scheme. This queueing model is applied to the operation of a battery swapping and charging station for electric vehicles (EVs). In addition to the LB scheme, we propose two congestion control policies based on EV queue length thresholds. With these policies, the model determines both EV-arrival and battery-supply intervals, and these depend on the number of EVs waiting in the queue. The queue length distributions, including those at arbitrary epochs, are derived using embedded Markov chain and supplementary variable methods. Performance measures such as blocking probability and mean waiting time are investigated using numerical examples. We study the characteristics of the system using numerical examples and use a cost analysis to investigate situations in which the application of each congestion control policy is advantageous.

scholarly journals A M/M/1 Queueing Network with Classical Retrial Policy

2021 ◽  
Vol 12 (1S) ◽  
pp. 329-337
Author(s):  
S. Shanmugasundaram, Et. al.
Keyword(s):  
Steady State ◽  
Queue Length ◽  
Queueing Network ◽  
State Probability ◽  
Queueing Model ◽  
Steady State Probability ◽  
Numerical Examples ◽  
System Length ◽  
Number Of Customers ◽  
Little's Formula

In this paper we study the M/M/1 queueing model with retrial on network. We derive the steady state probability of customers in the network, the average number of customers in the all the three nodes in the system, the queue length, system length using little’s formula. The particular case is derived (no retrial). The numerical examples are given to test the correctness of the model.

scholarly journals Performance Analysis of Novel Overload Control with Threshold Mechanism

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Doo Il Choi ◽  
Dae-Eun Lim
Keyword(s):  
Queue Length ◽  
Control Method ◽  
Length Distribution ◽  
Arrival Rate ◽  
Embedded Markov Chain ◽  
Overload Control ◽  
Queue Length Distribution ◽  
Markov Chain Method ◽  
Mean Waiting Time ◽  
Threshold Mechanism

We propose a novel overload control method with hysteresis property; that is, we analyze theM/G/1/Kqueueing system where the service and arrival rates are varied depending on the queue-length. We use two threshold values:L1(≤L2)andL2(≤K). When the queue-length increases by an amount betweenL1andL2, we apply one of the following two strategies to reduce the queue-length, either we decrease the mean service time or we decrease the arrival rate. If the queue-length exceedsL2with one strategy, we apply the other; thus, there are two models that depend on the method that was applied first. We derive the queue-length distribution at departure and at arbitrary epochs using the embedded Markov chain method and the supplementary variable method. We investigate performance measures including the loss probability and mean waiting time using various numerical examples.

ANALYTICAL APPROXIMATIONS FOR KITTING SYSTEMS WITH MULTIPLE INPUTS

2008 ◽  
Vol 25 (02) ◽  
pp. 187-216 ◽  
Author(s):  
RAM RAMAKRISHNAN ◽  
ANANTH KRISHNAMURTHY
Keyword(s):  
Queue Length ◽  
Control Policy ◽  
System Throughput ◽  
Multiple Components ◽  
Analytical Approximations ◽  
Mean Waiting Time ◽  
Computationally Intensive ◽  
Mean Queue Length ◽  
The Impact ◽  
Approximate Expressions

This research analyzes a kitting system where multiple components are grouped to form a predefined kit prior to assembly. The kitting system is modeled as a fork/join synchronization station and component supply is assumed to be from fabrication facilities operating under a kanban control policy. Exact analysis of these systems is computationally intensive even under Markovian assumptions. To evaluate the impact of input parameters on kitting system performance, several easily computable bounds on system throughput are first identified. Using these bounds, closed form approximate expressions for system throughput are derived. The throughput estimate is used to compute other performance measures of interest such as mean queue length and mean waiting time in the system. The accuracy of the approximations is validated using numerical experiments and some performance insights are given.

scholarly journals Performance Evaluation of Cloud Data Centers with Batch Task Arrivals

2013 ◽  
pp. 199-223 ◽  
Author(s):  
Hamzeh Khazaei ◽  
Jelena Mišić ◽  
Vojislav B. Mišić
Keyword(s):  
Performance Evaluation ◽  
Queue Length ◽  
Blocking Probability ◽  
General Distribution ◽  
Cloud Data ◽  
Wide Range ◽  
Accurate Performance ◽  
Cloud Data Centers ◽  
Poisson Arrivals

Accurate performance evaluation of cloud computing resources is a necessary prerequisite for ensuring that Quality of Service (QoS) parameters remain within agreed limits. In this chapter, the authors consider cloud centers with Poisson arrivals of batch task requests under total rejection policy; task service times are assumed to follow a general distribution. They describe a new approximate analytical model for performance evaluation of such systems and show that important performance indicators such as mean request response time, waiting time in the queue, queue length, blocking probability, probability of immediate service, and probability distribution of the number of tasks in the system can be obtained in a wide range of input parameters.

scholarly journals On the Effect of Finite Buffer Truncation in a Two-Node Jackson Network

2005 ◽  
Vol 42 (01) ◽  
pp. 199-222 ◽  
Author(s):  
Yutaka Sakuma ◽  
Masakiyo Miyazawa
Keyword(s):  
Stability Condition ◽  
Queue Length ◽  
Length Distribution ◽  
Buffer Size ◽  
Finite Buffer ◽  
Jackson Network ◽  
Numerical Examples ◽  
Queue Length Distribution ◽  
Special Cases ◽  
The Stability

We consider a two-node Jackson network in which the buffer of node 1 is truncated. Our interest is in the limit of the tail decay rate of the queue-length distribution of node 2 when the buffer size of node 1 goes to infinity, provided that the stability condition of the unlimited network is satisfied. We show that there can be three different cases for the limit. This generalizes some recent results obtained for the tandem Jackson network. Special cases and some numerical examples are also presented.

A single server tandem queue

1971 ◽  
Vol 8 (1) ◽  
pp. 95-109 ◽  
Author(s):  
Sreekantan S. Nair
Keyword(s):  
Waiting Time ◽  
Queue Length ◽  
Busy Period ◽  
Single Server ◽  
Queueing Model ◽  
Tandem Queue ◽  
Limiting Behavior ◽  
Virtual Waiting Time ◽  
Priority Model

Avi-Itzhak, Maxwell and Miller (1965) studied a queueing model with a single server serving two service units with alternating priority. Their model explored the possibility of having the alternating priority model treated in this paper with a single server serving alternately between two service units in tandem.Here we study the distribution of busy period, virtual waiting time and queue length and their limiting behavior.

Throughput maximization in a loss queueing system with heterogeneous servers

1990 ◽  
Vol 27 (03) ◽  
pp. 693-700 ◽  
Author(s):  
Matthew J. Sobel
Keyword(s):  
Queueing System ◽  
Blocking Probability ◽  
Cost Structure ◽  
Throughput Maximization ◽  
Queueing Model ◽  
Heterogeneous Servers ◽  
Waiting Room ◽  
Discounted Cost ◽  
Long Run ◽  
Poisson Arrivals

Assigning each arriving customer to the fastest idle server is shown to maximize throughput (equivalently, minimize blocking probability) in a queueing model with Poisson arrivals, heterogeneous exponential servers, and no waiting room. If a cost structure is imposed on this model, under specified conditions the same policy minimizes the expected discounted cost and the long-run average cost per unit time.

The disasters queue with working breakdowns and impatient customers

2020 ◽  
Vol 54 (3) ◽  
pp. 815-825
Author(s):  
Mian Zhang ◽  
Shan Gao
Keyword(s):  
Size Distribution ◽  
Performance Measures ◽  
Sojourn Time ◽  
Queue Length ◽  
Slow Rate ◽  
System Size ◽  
Impatient Customers ◽  
Numerical Examples ◽  
The Mean ◽  
Mean Queue Length

We consider the M/M/1 queue with disasters and impatient customers. Disasters only occur when the main server being busy, it not only removes out all present customers from the system, but also breaks the main server down. When the main server is down, it is sent for repair. The substitute server serves the customers at a slow rate(working breakdown service) until the main server is repaired. The customers become impatient due to the working breakdown. The system size distribution is derived. We also obtain the mean queue length of the model and mean sojourn time of a tagged customer. Finally, some performance measures and numerical examples are presented.

Controlled queues in heavy traffic

1975 ◽  
Vol 7 (3) ◽  
pp. 656-671 ◽  
Author(s):  
John H. Rath
Keyword(s):  
Diffusion Process ◽  
Queue Length ◽  
Queueing System ◽  
Systems Approach ◽  
Heavy Traffic ◽  
Queueing Systems ◽  
Control Policy ◽  
Controlled Diffusion ◽  
Controlled Queues

This paper studies a controlled queueing system in which the decisionmaker may change servers according to rules which depend only on the queue length. It is proved that for a given control policy a properly normalised sequence of these controlled queue length processes converges weakly to a controlled diffusion process as the queueing systems approach a state of heavy traffic.

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