Influence of relative traffic distribution in nodes with blocking: an analytical model

In nodes where the arriving packets are stored in one common buffer, packets with a given destination may have to wait for the transmission of packets with other destinations, even when the corresponding output channel is free. Although this so-called blocking effect has attracted considerable attention in literature, the influence of the relative distribution of the traffic according to destination has been largely overlooked. We therefore develop and analyze an appropriate discrete-time queueing model for a node whereby all arriving packets are accommodated in one common buffer and with two output channels that lead to distinct destinations. We study the stability of and the number of packets in the node. We then compare these results with those obtained for an analogous node with individual buffers for the distinct output channels. We demonstrate that the relative distribution of the traffic according to destination can have a major impact on the blocking effect and hence on the overall performance of the node

A two-class queueing model with class clustering and global FCFS service discipline

This paper considers a continuous-time queueing model with two types (classes) of customers each having their own dedicated server with exponential service times. The system adopts a "global FCFS" service discipline, i.e., all arriving customers are accommodated in one single FCFS queue, regardless of their types. "Class clustering" ,i.e., customers of any given type may (or may not) have a tendency to "arrive back-to-back", is a concept that we believe is often neglected in literature, but as it is clear that customers of different types hinder each other more as they tend to arrive in the system more clustered according to class in our system, the major aim of this paper is to estimate the impact of the degree of class clustering in our system. The motivation of our work are systems where this kind of blocking is encountered, such as input-queueing network switches or road splits

Effect of global FCFS and relative load distribution in two-class queues with dedicated servers

In this paper, we investigate multi-class multi-server queueing systems with global FCFS policy, i.e., where customers requiring different types of service— provided by distinct servers— are accommodated in one common FCFS queue. In such scenarios, customers of one class (i.e., requiring a given type of service) may be hindered by customers of other classes. The purpose of this paper is twofold: to gain (qualitative and quantitative) insight into the impact of (i) the global FCFS policy and (ii) the relative distribution of the load amongst the customer classes, on the system performance. We therefore develop and analyze an appropriate discrete-time queueing model with general independent arrivals, two (independent) customer classes and two class-specific servers.We study the stability of the system and derive the system-content distribution at random slot boundaries; we also obtain mean values of the system content and the customer delay, both globally and for each class individually. We then extensively compare these results with those obtained for an analogous system without global FCFS policy (i.e., with individual queues for the two servers). We demonstrate that global FCFS, as well as the relative distribution of the load over the two customer classes, may have a major impact on the system performance

Boundary problem in a system with global FCFS and presorting

In this paper we consider a continuous-time queueing system with two different types (1 and 2) of customers with two dedicated servers (also named 1 and 2). This means server 1 (2) can only serve customers of type 1 (2). The goal of this paper is to study the boundary conditions for a system with global FCFS and presorting service discipline, i.e., all arriving customers are accommodated in one single FCFS queue, regardless of their types, with an exception of the first N customers. For the first N customers the FCFS rule holds only within the types, i.e. customers of different types can overtake each other in order to be served. The motivation for our work comes from traffic and is to be able to give advise about the optimal length of filter lanes, i.e. lanes reserved for vehicles making a specific turn at a junction. This paper is a first step in this process

Influence of data clustering on in-order multi-core processing systems

In multi-core in-order processing systems, only one core can be utilized when the instruction at the head of the instruction queue produces data input for the next instruction in the queue. Although in-order processing has been studied in the past, the influence of data clustering, i.e., the extent to which subsequent instructions rely on each other's data, has been largely overlooked. We therefore develop a queueing model and provide closed-form formulae for the stability condition and the average time before instructions are executed. These expressions clearly reflect that data clustering can have a devastating impact

A continuous-time queueing model with class clustering and global FCFS service discipline

In this paper the focus is on "class clustering" in a continuous-time queueing model with two classes and dedicated servers. "Class clustering" means that customers of any given type may (or may not) have a tendency to "arrive back-to-back". We believe this is a concept that is often neglected in literature and we want to show that it can have a considerable impact on multiclass queueing systems, especially on the system considered in this paper. This system adopts a "global FCFS" service discipline, i.e., all arriving customers are accommodated in one single FCFS queue, regardless of their types. The major aim of our paper is to quantify the intuitively expected (due to the service discipline) negative impact of "class clustering" on the performance measures of our system. The motivation of our work are systems where this kind of inherent blocking is encountered, such as input-queueing network switches, road splits or security checks at airports