Social optimization in M/M/1 queue with working vacation and N-policy

2018 ◽  
Vol 52 (2) ◽  
pp. 439-452 ◽  
Author(s):  
Qing-Qing Ma ◽  
Ji-Hong Li ◽  
Wei-Qi Liu
Keyword(s):  
Social Welfare ◽  
Queue Length ◽  
Service Rate ◽  
Working Vacation ◽  
Stationary Probability Distribution ◽  
The Social ◽  
The Mean ◽  
Working Vacations ◽  
Mean Queue Length ◽  
The Impact

This paper deals with the N-policy M/M/1 queueing system with working vacations. Once the system becomes empty, the server begins a working vacation and works at a lower service rate. The server resumes regular service when there are N or more customers in the system. By solving the balance equations, the stationary probability distribution and the mean queue length under observable and unobservable cases are obtained. Based on the reward-cost structure and the theory of Markov process, the social welfare function is constructed. Finally, the impact of several parameters and information levels on the mean queue length and social welfare is illustrated via numerical examples, comparison work shows that queues with working vacations(WV) and N-policy have advantage in controlling the queue length and improving the social welfare.

Queues with time-dependent arrival rates. III — A mild rush hour

1968 ◽  
Vol 5 (3) ◽  
pp. 591-606 ◽  
Author(s):  
G. F. Newell
Keyword(s):  
Queueing Theory ◽  
Queue Length ◽  
Arrival Rate ◽  
Time Dependent ◽  
Service Rate ◽  
Diffusion Approximations ◽  
Dimensionless Form ◽  
Queue Lengths ◽  
The Mean ◽  
Mean Queue Length

The arrival rate of customers to a service facility is assumed to have the form λ(t) = λ(0) — βt2 for some constant β. Diffusion approximations show that for λ(0) sufficiently close to the service rate μ, the mean queue length at time 0 is proportional to β–1/5. A dimensionless form of the diffusion equation is evaluated numerically from which queue lengths can be evaluated as a function of time for all λ(0) and β. Particular attention is given to those situations in which neither deterministic queueing theory nor equilibrium stochastic queueing theory apply.

Queues with time-dependent arrival rates. III — A mild rush hour

1968 ◽  
Vol 5 (03) ◽  
pp. 591-606 ◽  
Author(s):  
G. F. Newell
Keyword(s):  
Queueing Theory ◽  
Queue Length ◽  
Arrival Rate ◽  
Time Dependent ◽  
Service Rate ◽  
Diffusion Approximations ◽  
Dimensionless Form ◽  
Queue Lengths ◽  
The Mean ◽  
Mean Queue Length

The arrival rate of customers to a service facility is assumed to have the formλ(t) =λ(0) —βt2for some constantβ.Diffusion approximations show that forλ(0) sufficiently close to the service rateμ, the mean queue length at time 0 is proportional toβ–1/5. A dimensionless form of the diffusion equation is evaluated numerically from which queue lengths can be evaluated as a function of time for allλ(0) andβ.Particular attention is given to those situations in which neither deterministic queueing theory nor equilibrium stochastic queueing theory apply.

Exponential upper bounds via martingales for multiplexers with Markovian arrivals

1994 ◽  
Vol 31 (4) ◽  
pp. 1049-1060 ◽  
Author(s):  
E. Buffet ◽  
N. G. Duffield
Keyword(s):  
Markov Processes ◽  
Queue Length ◽  
Heavy Traffic ◽  
Upper Bounds ◽  
Service Rate ◽  
Service Requirement ◽  
Atm Multiplexer ◽  
The Mean ◽  
Analytic Expression ◽  
Mean Queue Length

We obtain explicit upper bounds in closed form for the queue length in a slotted time FCFS queue in which the service requirement is a sum of independent Markov processes on the state space {0, 1}, with integral service rate. The bound is of the form [queue length for any where c < 1 and y > 1 are given explicitly in terms of the parameters of the model. The model can be viewed as an approximation for the burst-level component of the queue in an ATM multiplexer. We obtain heavy traffic bounds for the mean queue length and show that for typical parameters this far exceeds the mean queue length for independent arrivals at the same load. We compare our results on the mean queue length with an analytic expression for the case of unit service rate, and compare our results on the full distribution with computer simulations.

Exponential upper bounds via martingales for multiplexers with Markovian arrivals

1994 ◽  
Vol 31 (04) ◽  
pp. 1049-1060 ◽  
Author(s):  
E. Buffet ◽  
N. G. Duffield
Keyword(s):  
Markov Processes ◽  
Queue Length ◽  
Heavy Traffic ◽  
Upper Bounds ◽  
Service Rate ◽  
Service Requirement ◽  
Atm Multiplexer ◽  
The Mean ◽  
Analytic Expression ◽  
Mean Queue Length

We obtain explicit upper bounds in closed form for the queue length in a slotted time FCFS queue in which the service requirement is a sum of independent Markov processes on the state space {0, 1}, with integral service rate. The bound is of the form [queue length for any where c &lt; 1 and y &gt; 1 are given explicitly in terms of the parameters of the model. The model can be viewed as an approximation for the burst-level component of the queue in an ATM multiplexer. We obtain heavy traffic bounds for the mean queue length and show that for typical parameters this far exceeds the mean queue length for independent arrivals at the same load. We compare our results on the mean queue length with an analytic expression for the case of unit service rate, and compare our results on the full distribution with computer simulations.

scholarly journals Perturbation analysis of a variable M/M/1 queue: a probabilistic approach

2006 ◽  
Vol 38 (01) ◽  
pp. 263-283 ◽  
Author(s):  
Nelson Antunes ◽  
Christine Fricker ◽  
Fabrice Guillemin ◽  
Philippe Robert
Keyword(s):  
Power Series ◽  
Busy Period ◽  
Stationary Process ◽  
Probabilistic Approach ◽  
Power Series Expansion ◽  
Mean Value ◽  
Service Rate ◽  
The Mean ◽  
The Impact ◽  
Period Duration

In this paper, motivated by the problem of the coexistence on transmission links of telecommunications networks of elastic and unresponsive traffic, we study the impact on the busy period of an M/M/1 queue of a small perturbation in the service rate. The perturbation depends upon an independent stationary process (X(t)) and is quantified by means of a parameter ε ≪ 1. We specifically compute the two first terms of the power series expansion in ε of the mean value of the busy period duration. This allows us to study the validity of the reduced service rate approximation, which consists in comparing the perturbed M/M/1 queue with the M/M/1 queue whose service rate is constant and equal to the mean value of the perturbation. For the first term of the expansion, the two systems are equivalent. For the second term, the situation is more complex and it is shown that the correlations of the environment process (X(t)) play a key role.

Conceptualizing the Social Economy in China

2012 ◽  
Vol 47 (3) ◽  
pp. 1083-1123 ◽  
Author(s):  
LI ZHAO
Keyword(s):  
Social Welfare ◽  
Political Institutions ◽  
Poverty Reduction ◽  
Social Economy ◽  
Welfare System ◽  
Cultural Traditions ◽  
For Profit ◽  
Social Welfare System ◽  
The Social ◽  
The Impact

AbstractThis study offers a conceptual analysis of the social economy in China within the context of institutional transition. In China, economic reform has engendered significant social changes. Accelerated economic growth, privatization of the social welfare system, and the rise of civil society explain the institutional contexts in which a range of not-for-profit initiatives, neither state-owned nor capital-driven, re-emerged. They are defined in this research as the social economy in China. This study shows that although the term itself is quite new, the social economy is no new phenomenon in China, as its various elements have a rich historical tradition. Moreover, the impact of the transition on the upsurge of the Chinese social economy is felt not only through direct means of de-nationalization and marketization and, as a consequence, the privatization of China's social welfare system, but also through various indirect means. The development of the social economy in China was greatly influenced by the framework set by political institutions and, accordingly, legal enabling environments. In addition, the link to the West, as well as local historical and cultural traditions, contribute towards explaining its re-emergence. Examining the practices in the field shows that the social economy sector in China is conducive to achieving a plural economy and an inclusive society, particularly by way of poverty reduction, social service provision, work integration, and community development. Therefore, in contemporary China, it serves as a key sector for improving welfare, encouraging participation, and consolidating solidarity.

International Social Work and Social Welfare: Central America

2013 ◽  
Author(s):  
Maria Julia
Keyword(s):  
Social Work ◽  
Social Welfare ◽  
Central America ◽  
International Social Work ◽  
Political Processes ◽  
New Approaches ◽  
Political Events ◽  
The Social ◽  
The Impact ◽  
International Social

The social, political, and economic features of Central America are summarized and the impact of economic and political processes on the region is highlighted. Predominant global, historical, cultural, and political events are weaved together, in an attempt to understand the realities of the region. The challenges for social work profession and practice are presented, as well as their implications for new approaches to intervention and education.

scholarly journals An M/M/1 Queue with Working Vacation and Vacation Interruption Under Bernoulli Schedule

2018 ◽  
Vol 7 (4.10) ◽  
pp. 448
Author(s):  
P. Manoharan ◽  
A. Ashok
Keyword(s):  
Geometric Approach ◽  
Stochastic Decomposition ◽  
Working Vacation ◽  
System Parameters ◽  
Mean Waiting Time ◽  
The Mean ◽  
Vacation Interruption ◽  
Mean Queue Length ◽  
Vacation Period ◽  
Bernoulli Schedule

This work deals with M/M/1 queue with Vacation and Vacation Interruption Under Bernoulli schedule. When there are no customers in the system, the server takes a classical vacation with probability p or a working vacation with probability 1-p, where . At the instants of service completion during the working vacation, either the server is supposed to interrupt the vacation and returns back to the non-vacation period with probability 1-q or the sever will carry on with the vacation with probability q. When the system is non empty after the end of vacation period, a new non vacation period begins. A matrix geometric approach is employed to obtain the stationary distribution for the mean queue length and the mean waiting time and their stochastic decomposition structures. Numerous graphical demonstrations are presented to show the effects of the system parameters on the performance measures.  

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