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...

In this paper a finite capacity, loss and delay, interdependent queueing system with controllable arrival rates and no passing has been considered. For this model, the steady state probabilities are derived and the average waiting times for the two types of customers (elective and emergency) are obtained for varying arrival rates when the arrival and service processes are interdependent. Numeri...

We develop a queueing model for an appointment-based service system that consists of two queues in tandem: the appointment queue followed by the service queue. Customers join the appointment queue when they call for appointments, stay there (not physically) until the appointment time comes, and then leave the appointment queue and may physically join the service queue, and wait there until serv...

this paper presents a discrete-time single-server finite buffer n threshold policy queue with renewal input and discretemarkovian service process. the server terminates service whenever the system becomes empty, and recommencesservice as soon as the number of waiting customers in the queue is n. we obtain the system-length distributionsat pre-arrival and arbitrary epochs using the supplementary...

In this paper, we consider a single server queueing system in which the arrivals occur according to Markovian arrival process (MAP). The served customers may be recruited (or opted from those customers’ point of view) act as secondary servers provide services waiting customers. Such who are referred servers. service times main well that assumed exponentially distributed possibly with different ...

Consider a two-server, ordered entry, queuing system with heterogeneous servers and finite waiting rooms in front of the servers. Service times are negative exponentially distributed. The arrival process is deterministic. A matrix solution for the steady state probabilities of the number of customers in the system is derived. The overflow probability will be used to formulate the stability cond...

We consider the M/M/N/N+R service system, characterized by N servers, R waiting positions, Poisson arrivals and exponential service times. We discuss representations and bounds for the rate of convergence to stationarity of the number of customers in the system, and study its behaviour as a function of R, N and the arrival rate λ, allowing λ to be a function of N.

Consider a network facility location problem where congestion arises at facilities, and is represented by delay functions that approximate the queueing process. We strive to minimize the sum of customers' transportation and waiting times, and facilities' xed and variable costs. The problem is solved using a column generation technique within a Branch-and-Bound scheme. Numerical results are repo...

We consider a polling system where the server cyclically serves the queues according to the following discipline: the server does one round of visits to the queues applying the gated service discipline at each of the queues, followed by one round of visits applying the exhaustive service discipline at each of the queues, and this alternating pattern repeats itself. We call this the Gated/Exhaus...