# Queueing Systems

## List of Papers (Total 106)

#### Joint queue length distribution of multi-class, single-server queues with preemptive priorities

In this paper we analyze an M/M/1 queueing system with an arbitrary number of customer classes, with class-dependent exponential service rates and preemptive priorities between classes. The queuing system can be described by a multi-dimensional Markov process, where the coordinates keep track of the number of customers of each class in the system. Based on matrix-analytic...

#### Concave switching in single-hop and multihop networks

Switched queueing networks model wireless networks, input-queued switches, and numerous other networked communications systems. We consider an ($$\alpha ,g$$)-switch policy; these policies provide a generalization of the MaxWeight policies of Tassiulas and Ephremides (IEEE Trans Autom Control 37(12):4936–1948, 1992) and the weighted $$\alpha$$-fair with allocations of Mo and...

#### A coupled processor model with simultaneous arrivals and ordered service requirements

We study a coupled processor model with simultaneous arrivals. Under the assumption of ordered input, the Laplace–Stieltjes transform of the joint stationary amount of work in the system can be explicitly calculated by relating it to the amount of work in a parallel queueing system without coupling. This relation is first exploited for the system with two coupled queues. The...

#### On the scalability and message count of Trickle-based broadcasting schemes

As the use of wireless sensor networks increases, the need for efficient and reliable broadcasting algorithms grows. Ideally, a broadcasting algorithm should have the ability to quickly disseminate data, while keeping the number of transmissions low. In this paper, we analyze the popular Trickle algorithm, which has been proposed as a suitable communication protocol for code...

#### Perfect sampling of a single-server queue with periodic Poisson arrivals

In this paper we present algorithms for the perfect sampling of single-server time-varying queues with periodic Poisson arrivals under the first come first served (FCFS) discipline. The service durations have periodically time-dependent exponential ($$\mathrm M _t/\mathrm M _t/1$$) or homogeneous general ($$\mathrm M _t/\mathrm G /1$$) distributions. Assuming a cycle length of 1...

#### Service-time ages, residuals, and lengths in an $$M/GI/\infty$$ service system

Important supplementary variables of a stationary $$M/GI/\infty$$ service system are the service-time ages, residuals, and lengths of the customers present in the system at time $$0$$. Our main result for a stationary system is that these times form a Poisson processes on $$R_+^3$$. Thus, by the order statistic property of Poisson processes, the three-dimensional vectors of the...

#### Waiting time distributions in the accumulating priority queue

We are interested in queues in which customers of different classes arrive to a service facility, and where performance targets are specified for each class. The manager of such a queue has the task of implementing a queueing discipline that results in the performance targets for all classes being met simultaneously. For the case where the performance targets are specified in...

#### Hitting time in Erlang loss systems with moving boundaries

When the boundary—the total number of servers— in an Erlang loss system is a function of time, customers may also be lost due to boundary variations. On condition that these customers are selected independently of their history, we solve for the hitting-time distribution and transient distribution of busy servers. We derive concise asymptotic expressions in the time domain for...

#### The strong weak convergence of the quasi-EA

In this paper, we investigate the convergence of a novel simulation scheme to the target diffusion process. This scheme, the Quasi-EA, is closely related to the Exact Algorithm (EA) for diffusion processes, as it is obtained by neglecting the rejection step in EA. We prove the existence of a myopic coupling between the Quasi-EA and the diffusion. Moreover, an upper bound for the...

#### The G t /GI/s t +GI many-server fluid queue

This paper introduces a deterministic fluid model that approximates the many-server G t /GI/s t +GI queueing model, and determines the time-dependent performance functions. The fluid model has time-varying arrival rate and service capacity, abandonment from queue, and non-exponential service and patience distributions. Two key assumptions are that: (i) the system alternates...

#### A performance analysis of channel fragmentation in dynamic spectrum access systems

Dynamic Spectrum Access systems offer temporarily available spectrum to opportunistic users capable of spreading transmissions over a number of non-contiguous subchannels. Such methods can be highly beneficial in terms of spectrum utilization, but excessive fragmentation degrades performance and hence off-sets the benefits. To get some insight into acceptable levels of...

#### Repair systems with exchangeable items and the longest queue mechanism

We consider a repair facility consisting of one repairman and two arrival streams of failed items, from bases 1 and 2. The arrival processes are independent Poisson processes, and the repair times are independent and identically exponentially distributed. The item types are exchangeable, and a failed item from base 1 could just as well be returned to base 2, and vice versa. The...

#### Strong stationary duality for Möbius monotone Markov chains

For Markov chains with a finite, partially ordered state space, we show strong stationary duality under the condition of Möbius monotonicity of the chain. We give examples of dual chains in this context which have no downwards transitions. We illustrate general theory by an analysis of nonsymmetric random walks on the cube with an interpretation for unreliable networks of queues.

#### Sojourn times in a processor sharing queue with multiple vacations

We study an M/G/1 processor sharing queue with multiple vacations. The server only takes a vacation when the system has become empty. If he finds the system still empty upon return, he takes another vacation, and so on. Successive vacations are identically distributed, with a general distribution. When the service requirements are exponentially distributed we determine the...

#### A product form solution to a system with multi-type jobs and multi-type servers

We consider a memoryless single station service system with servers $$\mathcal{S}=\{m_{1},\ldots,m_{K}\}$$, and with job types $$\mathcal{C}=\{a,b,\ldots\}$$. Service is skill-based, so that server m i can serve a subset of job types $$\mathcal{C}(m_{i})$$. Waiting jobs are served on a first-come-first-served basis, while arriving jobs that find several idle servers are assigned...