Queue Content Research Articles

“Please Hold for the Next Available Agent:” The Effect of Hold Queue Content on Apparent Hold duration

This paper describes a study of the effects of four types of content presentation for consumers waiting on-hold to speak to a call center agent. Of particular interest was the interactive voice portal (IVP) condition in which callers used a voice portal to retrieve news and other information while they waited on hold in a queue. An experiment explored the effect of four content types (Silence, Music, Advertisements, and Interactive Voice Portal) on callers' estimates of on-hold duration across four hold intervals (60, 120, 240, and 480 seconds) and for three customer tasks. The dependent measures were hold-time estimation error and customer satisfaction ratings. Each participant placed four calls to a simulated call center in which they were presented with one of the four content types and hold durations. Both Content and Hold Time had a significant effect on estimation error and customer satisfaction. The interactive voice portal yielded the best results overall, suggesting an interesting new approach to call center hold queues.

Automatically Verifying Concurrent Queue Algorithms

Concurrent FIFO queues are a common component of concurrent systems. Using a single shared lock to prevent concurrent manipulations of queue contents reduces system concurrency. Therefore, many algorithms were suggested to increase concurrency while maintaining the correctness of queue manipulations. This paper shows how to automatically verify partial correctness of concurrent FIFO queue algorithms using existing abstract interpretation techniques. In particular, we verify all the safety properties originally specified for two concurrent queue algorithms without imposing an a priori bound on the number of allocated objects and threads.

Analysis of a discrete-time GI–G–1 queueing model subjected to bursty interruptions

In this contribution, we investigate a discrete-time single-server queue subjected to server interruptions generated by a 2-state Markov process. The model under consideration assumes customers with multiple-slot service times, which leads to the introduction of two different service strategies depending on whether service of an interrupted customer continues or restarts after an interruption. For both alternatives, we establish expressions for the steady-state probability generating functions of the buffer contents, the unfinished work and the customer delay in terms of the effective customer service times. From these results, closed-form expressions for various performance measures, such as the moments of these quantities, can be established. After dealing with some stability issues, we illustrate the impact of both service strategies on the buffer performance with some numerical examples. Scope and purpose Discrete-time queueing theory is distinguished from its more developed continuous-time counterpart by the synchronous nature of its service. Time is divided into fixed-length slots and service of a customer typically takes an integer number of slots. Discrete-time queueing models are particularly appropriate to describe the various queueing related phenomena in digital computer and communication systems including mobile and B-ISDN networks based on asynchronous transfer mode (ATM) technology, due to the packetized nature of these transport protocols. This work focuses on a discrete-time queueing system with server interruptions. Interruptions are an abstraction of temporary server unavailability. The latter can be caused by temporary occupancy of the server by other customers — regulated by a scheduling discipline such as round robin or priority scheduling — or temporary failure of the server (e.g. due to transmission errors, maintenance or repair). Typically, interruptions occurring in these systems have a bursty nature, i.e., they occur in bursts rather than being randomly spread over time. The presented model allows to study the effects of the burstiness of the server interruptions on various performance measures such as mean queue contents and mean customer delay. Two different operation strategies are hereby considered: after an interruption, service may either continue where it left off or it may completely restart.

Network of Single-Server Queues with Dependent Service Times

A network of single-server nodes fed by customers of several classes is considered. Each customer is equipped with the random work to be done for completing service. The distribution of this work and the rate of its decreasing during the service depend on the node, the class of the customer, the queue contents and the residual work loads of the customers at the node. The service discipline is LCFS preemptive-resume. For both open and closed network, the stationary distribution is derived. In general, this distribution is not a product form. For the open network, sufficient conditions yielding the product form are given. For both open and closed network, sufficient invariance conditions are found.

Large buffer asymptotics for the queue with fractional Brownian input

In this paper, a strong asymptotic estimate for the queue content distribution of a fluid queue fed by a fractional Brownian input with Hurst parameter H ∊ [1/2,1[is studied. By applying general results on suprema of centred Gaussian processes, in particular, we show that for large x. Explicit formulae for constants κ, γ and L are given in terms of H and system parameters.

Large buffer asymptotics for the queue with fractional Brownian input

In this paper, a strong asymptotic estimate for the queue content distribution of a fluid queue fed by a fractional Brownian input with Hurst parameter H ∊ [1/2,1[is studied. By applying general results on suprema of centred Gaussian processes, in particular, we show that for large x. Explicit formulae for constants κ, γ and L are given in terms of H and system parameters.

Large buffer asymptotics for the queue with fractional Brownian input

In this paper, a strong asymptotic estimate for the queue content distribution of a fluid queue fed by a fractional Brownian input with Hurst parameter H ∊ [1/2,1[is studied. By applying general results on suprema of centred Gaussian processes, in particular, we show that for large x. Explicit formulae for constants κ, γ and L are given in terms of H and system parameters.

Subexponential loss rates in a GI/GI/1 queue with applications

Consider a single server queue with i.i.d. arrival and service processes, \{A,\ A_n,n\geq 0\} and \{C,\ C_n,n\geq 0\}, respectively, and a finite buffer B. The queue content process \{Q^B_n,\ n\geq 0\} is recursively defined as Q^B_{n+1}=\min((Q^B_n+A_{n+1}-C_{n+1})^+,B), q^+=\max(0,q). When \mathbb{E}(A-C)<0, and A has a subexponential distribution, we show that the stationary expected loss rate for this queue \mathbb{E}(Q^B_n+A_{n+1}-C_{n+1}-B)^+ has the following explicit asymptotic characterization: \mathbb{E}(Q^B_n+A_{n+1}-C_{n+1}-B)^+\sim \mathbb{E}(A-B)^+ \quad \hbox{as} \ B\rightarrow \infty, independently of the server process C_n. For a fluid queue with capacity c, M/G/\infty arrival process A_t, characterized by intermediately regularly varying on periods \tau^{\mathrm{on}}, which arrive with Poisson rate \Lambda, the average loss rate \lambda_{\mathrm{loss}}^B satisfies {\lambda_{\mathrm{loss}}^B}\sim \Lambda \mathbb{E}(\tau^{\mathrm{on}}\eta-B)^+ \quad \hbox{as}\ B\rightarrow \infty, where \eta=r+\rho-c, \rho=\mathbb{E}A_ts r (c\leq r) is the rate at which the fluid is arriving during an on period. Accuracy of the above asymptotic relations is verified with extensive numerical and simulation experiments. These explicit formulas have potential application in designing communication networks that will carry traffic with long-tailed characteristics, e.g., Internet data services.

Symbolic protocol verification with queue BDDs

Symbolic verification based on Binary Decision Diagrams (BDDs) has proven to be a powerful technique for ensuring the correctness of digital hardware. In contrast, BDDs have not caught on as widely for software verification, partly because the data types used in software are more complicated than those used in hardware. In this work, we propose an extension of BDDs for dealing with dynamic data structures. Specifically, we focus on queues, since they are commonly used in modeling communication protocols. We introduce Queue BDDs (QBDDs) which include all the power of BDDs while also providing an efficient representation of queue contents. Experimental results show that QBDDs are well-suited for the verification of communication protocols.

Reducing run queue contention in shared memory multiprocessors

The performance of parallel processing systems, especially large systems, is sensitive to various types of overhead and contention. Performance consequences may be serious when contention occurs for hardware resources such as memory or the interconnection network. Contention can also occur for software resources such as critical data structures maintained by either system or application software. A run queue is one such critical data structure that can affect overall system performance. There are two basic types of run queues, centralized and distributed. Both present performance problems. There are also several techniques to mitigate their drawbacks, but none is completely satisfactory. Instead, the author proposes a different run queue organization, a hierarchical organization that inherits the best features of the centralized and the distributed queue organizations while avoiding their pitfalls. Thus, the hierarchical organization is suitable for building large-scale multiprocessor systems.

Heavy traffic analysis of a storage model with long range dependent On/Off sources

We consider a fluid queueing system with infinite storage capacity and constant output rate offered a superposition ofN identical On/Off sources, where the ratio of input to output rate is small. The On and/or Off periods have heavy tailed distributions with infinite variance, giving rise to Long Range Dependence in the arrival process. In the limit of a large number of sources and high load, it is shown that the tail of the stationary queue content distribution is Weibullian, implying much larger queue contents than in the classical case of exponential tails. Noting that similar results were recently found by I. Norros for a storage system input by a Fractional Brownian Motion, we then show how the two models are related, thus providing a further physical motivation for the Fractional Brownian Motion model.

A hierarchical task queue organization for shared-memory multiprocessor systems

There are two basic ways in which waiting ready tasks can be organized: centralized organization or distributed organization. In the centralized organization, a single central task queue is maintained. In the latter case, private ready queue of tasks. Ideally, a central ready queue global to all processors is desired over the distributed organization because the centralized organization provides perfect load sharing. However, the centralized organization is not suitable for large parallel systems because the central task queue could become a system bottleneck. The distributed organization, on the other hand, creates the load imbalance problem, which results in performance deterioration, while techniques have been proposed to reduce the ill-effects of task queue contention in the centralized organization and load imbalance in the distributed organization these techniques introduce problems of their own. We propose the use of a hierarchical task queue organization to incorporate the best features of these two organizations. Our study into the performance of this hierarchical organization shows that a properly designed hierarchical organization provides performance very close to that of the centralized organization while eliminating the ready queue contention problem, we also provide an analysis that identifies and provides guidance for designing the hierarchical task queue organization that avoids ready queue access contention. A brief discussion of task scheduling policies is also included. >

Markov-modulated flow model for the output queues of a packet switch

The output queues of an M*N packet switch are studied using a Markov-modulated flow model. The switching element is a central server which sequentially routes packets from the inputs to the outputs. The focus is on systems in which the server speed is such that the bulk of the queuing takes place in the output queues. The conventional point process approach neglects the impact of switching and transmission time. An attempt is made to account for these finite system speeds by using a Markov-modulated continuous flow to approximate the arrival process to an output queue. This model captures the dependency between arrivals at different outputs and reflects the fact that packet arrivals and departures are not instantaneous. The output queue content distribution is obtained, for both infinite and finite buffer systems, from the spectral expansion of the solution of a system of differential equations. Numerical examples and comparisons with the results of an M/M/1 approximation are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Transient and Stationary Distributions for Fluid Queues and Input Processes with a Density

Transient and stationary distributions of queue content for fluid queues whose continuous input process has a density with respect to time are studied. Results are obtained via a method primarily introduced by Benes, when considering input processes increasing by jumps at random times. The general formulas are applied to the queue where the input density varies as a stationary Ornstein-Uhlenbeck process. Such fluid queue models are useful in the field of telecommunications for dimensioning studies of packet multiplexers which are offered a superposition of variable bit rate video sources.

An Acknowledgement-Based Access Scheme in a Two-Node Packet-Radio Network

A two-node packet-radio network with infinite buffers at the nodes is considered. The two nodes transmit data packets to a common station through a shared radio channel. One of the two nodes is granted full access rights to the channel, while the other node bases its decisions whether to transmit or not on the acknowledgments it receives about its transmissions. For this acknowledgment-based access scheme and for general arrival processes, we derive the joint generating function of the queue contents in steady state, as well as the condition for steady state. From the generating function, any moment can be derived, as well as average time delays. Numerical results are presented for independent Bernoulli arrival processes.