Abstract: How to maintain the service speeds for the business
to make the biggest profit is a problem worthy of study, which is
discussed in this paper with the use of queuing theory. An M/M/1/N
queuing model with variable input rates, variable service rates and
impatient customers is established, and the following conclusions
are drawn: the stationary distribution of the model, the relationship
between the stationary distribution and the probability that there are n
customers left in the system when a customer leaves (not including
the customer who leaves himself), the busy period of the system,
the average operating cycle, the loss probability for the customers
not entering the system while they arriving at the system, the mean
of the customers who leaves the system being for impatient, the
loss probability for the customers not joining the queue due to the
limited capacity of the system and many other indicators. This paper
also indicates that the following conclusion is not correct: the more
customers the business serve, the more profit they will get. At last,
this paper points out the appropriate service speeds the business
should keep to make the biggest profit.
Abstract: We consider a network of two M/M/1 parallel queues having the same poisonnian arrival stream with rate λ. Upon his arrival to the system a customer heads to the shortest queue and stays until being served. If the two queues have the same length, an arriving customer chooses one of the two queues with the same probability. Each duration of service in the two queues is an exponential random variable with rate μ and no jockeying is permitted between the two queues. A new numerical method, based on linear programming and convex optimization, is performed for the computation of the steady state solution of the system.
Abstract: Main goal of preventive healthcare problems are at
decreasing the likelihood and severity of potentially life-threatening
illnesses by protection and early detection. The levels of
establishment and staffing costs along with summation of the travel
and waiting time that clients spent are considered as objectives
functions of the proposed nonlinear integer programming model. In
this paper, we have proposed a bi-objective mathematical model for
designing a network of preventive healthcare facilities so as to
minimize aforementioned objectives, simultaneously. Moreover, each
facility acts as M/M/1 queuing system. The number of facilities to be
established, the location of each facility, and the level of technology
for each facility to be chosen are provided as the main determinants
of a healthcare facility network. Finally, to demonstrate performance
of the proposed model, four multi-objective decision making
techniques are presented to solve the model.
Abstract: In this paper, genetic algorithm (GA) is proposed for
the design of an optimization algorithm to achieve the bandwidth
allocation of ATM network. In Broadband ISDN, the ATM is a highbandwidth;
fast packet switching and multiplexing technique. Using
ATM it can be flexibly reconfigure the network and reassign the
bandwidth to meet the requirements of all types of services. By
dynamically routing the traffic and adjusting the bandwidth
assignment, the average packet delay of the whole network can be
reduced to a minimum. M/M/1 model can be used to analyze the
performance.
Abstract: How to effectively allocate system resource to process
the Client request by Gateway servers is a challenging problem. In
this paper, we propose an improved scheme for autonomous
performance of Gateway servers under highly dynamic traffic loads.
We devise a methodology to calculate Queue Length and Waiting
Time utilizing Gateway Server information to reduce response time
variance in presence of bursty traffic. The most widespread
contemplation is performance, because Gateway Servers must offer
cost-effective and high-availability services in the elongated period,
thus they have to be scaled to meet the expected load. Performance
measurements can be the base for performance modeling and
prediction. With the help of performance models, the performance
metrics (like buffer estimation, waiting time) can be determined at
the development process. This paper describes the possible queue
models those can be applied in the estimation of queue length to
estimate the final value of the memory size. Both simulation and
experimental studies using synthesized workloads and analysis of
real-world Gateway Servers demonstrate the effectiveness of the
proposed system.