We consider a system consisting of a server serving in sequence a fixed number of stations. At each station there is an infinite queue of customers that have to undergo a preparation phase before being served. This model is connected to layered queuing networks, to an extension of polling systems, and surprisingly to random graphs. We are interested in the waiting time of the server. The waitin...

—In complex RIA (Rich Internet Application) environment, the browser may have to load and process very large amount of data, which may result in long waiting time and bad waiting experience. This may even cause to lose customers for commercial sites. To avoid such problems, it is necessary to replace the natural logic algorithms with some optimization algorithms. In this paper, a combined algo...

Queueing theory is concerned with developing and investigating mathematical models of systems where customers wait for service. The terms customers and servers are generic. Customers could, for example, be humans waiting in a physical line or waiting on hold on the telephone, jobs waiting to be processed in a factory, or tasks waiting for processing in a computer or communication system. Exampl...

The M/M/1 retrial queue with working vacations and negative customers is introduced. The arrival processes of positive customers and negative customers are Poisson. Upon the arrival of a positive customer, if the server is busy the customer would enter an orbit of infinite size and the orbital customers send their requests for service with a constant retrial rate. The single server takes an exp...

The study sought to test the industry wide claim in fast-food restaurant that they deliver pizza within 10 minutes of waiting. further assess extent which actual waiting period for differs from perceived time. A sample 500 transactions had their order cycle time measured, and corresponding was also recorded surveyed respondents who initiated transactions. revealed there are statistically signif...

Credible queueing models of human services acknowledge human characteristics. A prevalent one is the ability of humans to abandon their wait, for example while waiting to be answered by a telephone agent, waiting for a physician’s checkup at an emergency department, or waiting for the completion of an Internet transaction. Abandonments can be very costly, to either the service provider (a forgo...

The paper considers multivariate discrete random sums with equal number of summands. Such distributions describe the total claim amount received by a company in a fixed time point. In Queuing theory they characterize cumulative waiting times of customers up to time t. In Theory of branching processes they model the number of heirs at a fixed point in time. Here some general properties and formu...

Consider a ring on which customers arrive according to a Poisson process. Arriving customers drop somewhere on the circle and wait there for a server who travels on the ring. Whenever this server encounters a customer, he stops and serves the customer according to an arbitrary service time distribution. After the service is completed, the server removes the client from the circle and resumes hi...

In service sector, there are challenges in keeping an optimum balance between customers' demand and availability of resources. This problem is going to be more intense in the health sector due to the fact that both arrival and service times are random. Therefore, designing the service environment by keeping the optimum balance between customers’ demand and available resources is becoming a seri...

We study a queueing network with a single shared server that serves the queues in a cyclic order. External customers arrive at the queues according to independent Poisson processes. After completing service, a customer either leaves the system or is routed to another queue. This model is very generic and finds many applications in computer systems, communication networks, manufacturing systems,...