Results 1  10
of
20
Coping with TimeVarying Demand When Setting Staffing Requirements for a Service System
, 2007
"... We review queueingtheory methods for setting staffing requirements in service systems where customer demand varies in a predictable pattern over the day. Analyzing these systems is not straightforward, because standard queueing theory focuses on the longrun steadystate behavior of stationary mode ..."
Abstract

Cited by 63 (25 self)
 Add to MetaCart
We review queueingtheory methods for setting staffing requirements in service systems where customer demand varies in a predictable pattern over the day. Analyzing these systems is not straightforward, because standard queueing theory focuses on the longrun steadystate behavior of stationary models. We show how to adapt stationary queueing models for use in nonstationary environments so that timedependent performance is captured and staffing requirements can be set. Relatively little modification of straightforward stationary analysis applies in systems where service times are short and the targeted quality of service is high. When service times are moderate and the targeted quality of service is still high, timelag refinements can improve traditional stationary independent periodbyperiod and peakhour approximations. Timevarying infiniteserver models help develop refinements, because closedform expressions exist for their timedependent behavior. More difficult cases with very long service times and other complicated features, such as endofday effects, can often be treated by a modifiedofferedload approximation, which is based on an associated infiniteserver model. Numerical algorithms and deterministic fluid models are useful when the system is overloaded for an extensive period of time. Our discussion focuses on telephone call centers, but applications to police patrol, banking, and hospital emergency rooms are also mentioned.
The analysis of queues with timevarying rates for telecommunication models
 Telecommunication Systems
, 2002
"... Abstract. Time dependent behavior has an impact on the performance of telecommunication models. Examples include: staffing a call center, pricing the inventory of private line services for profit maximization, and measuring the time lag between the peak arrivals and peak load for a system. These pro ..."
Abstract

Cited by 14 (0 self)
 Add to MetaCart
(Show Context)
Abstract. Time dependent behavior has an impact on the performance of telecommunication models. Examples include: staffing a call center, pricing the inventory of private line services for profit maximization, and measuring the time lag between the peak arrivals and peak load for a system. These problems and more motivate the development of a queueing theory with time varying rates. Queueing theory as discussed in this paper is organized and presented from a communications perspective. Canonical queueing models with timevarying rates are given and the necessary mathematical tools are developed to analyze them. Finally, we illustrate the use of these models through various communication applications.
A Nonstationary OfferedLoad Model for Packet Networks
, 1998
"... Motivated by the desire to model complex features of network traffic revealed in traffic measurements, such as heavytail probability distributions, longrange dependence, self similarity and nonstationarity, we propose a nonstationary offeredload model, in which connections of multiple types arriv ..."
Abstract

Cited by 13 (2 self)
 Add to MetaCart
Motivated by the desire to model complex features of network traffic revealed in traffic measurements, such as heavytail probability distributions, longrange dependence, self similarity and nonstationarity, we propose a nonstationary offeredload model, in which connections of multiple types arrive according to independent nonhomogeneous Poisson processes, and general bandwidth stochastic processes describe the individual user bandwidth requirements at multiple links of a communication network during their connections. For example, an individual bandwidth process may be an onoff process where the on and off times have general (possibly heavytail) distributions. We obtain expressions for the moment generating function, mean and variance of the total required bandwidth of all customers on each link at any designated time. We suggest making decisions based on the probability that demand will exceed supply, or other designated target level, at each time of interest, using (i) numerical...
Realtime delay estimation based on delay history
, 2007
"... Motivated by interest in making delay announcements to arriving customers who must wait in call centers and related service systems, we study the performance of alternative realtime delay estimators based on recent customer delay experience. The main estimators considered are: (i) the delay of the ..."
Abstract

Cited by 12 (4 self)
 Add to MetaCart
Motivated by interest in making delay announcements to arriving customers who must wait in call centers and related service systems, we study the performance of alternative realtime delay estimators based on recent customer delay experience. The main estimators considered are: (i) the delay of the last customer to enter service (LES), (ii) the delay experienced so far by the customer at the head of the line (HOL), and (iii) the delay experienced by the customer to have arrived most recently among those who have already completed service (RCS). We compare these delayhistory estimators to the estimator based on the queue length (QL), which requires knowledge of the mean interval between successive service completions in addition to the queue length. We characterize performance by the mean squared error (MSE). We do analysis and conduct simulations for the standard GI/M/s multiserver queueing model, emphasizing the case of large s. We obtain analytical results for the conditional distribution of the delay given the observed HOL delay. An approximation to its mean value serves as a refined estimator. For all three candidate delay estimators, the MSE relative to the square of the mean is asymptotically negligible in the manyserver and classical heavytraffic limiting regimes.
Connectivity Dynamics for Vehicular AdHoc Networks
 in Signalized Road Systems," International Teletraffic Congress (ITC
, 2009
"... Abstract – In this paper, we analyze the connectivity dynamics of vehicular adhoc networks in a generic signalized urban route. Given the velocity profile of an urban route as a function of space and time, we utilize a fluid model to characterize the general vehicular traffic flow, and a stochastic ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
(Show Context)
Abstract – In this paper, we analyze the connectivity dynamics of vehicular adhoc networks in a generic signalized urban route. Given the velocity profile of an urban route as a function of space and time, we utilize a fluid model to characterize the general vehicular traffic flow, and a stochastic model to capture the randomness of individual vehicle. From the fluid and stochastic models, we can acquire respectively the densities of the mean number of vehicles along the road and the corresponding distribution. With the knowledge of the vehicular density dynamics, we determine the probability that the communication network is fully connected, i.e., each node can communicate with every other node through a multihop path, and the problem is also investigated for a general case of a kconnected network. To closely approximate the practical road conditions, we use a densitydependent velocity profile to approximate vehicle interactions and capture the shockwave propagation at traffic signals. We confirm the accuracy of the connectivity analysis through simulations and show that the analytical results are good approximations even when vehicles interact with each other as their movement is controlled by traffic lights. We also illustrate that system engineering and planning for optimizing connectivity in the communication networks can be carried out with the results in this paper.
Stabilizing Performance in a SingleServer Queue with TimeVarying Arrival Rate
, 2014
"... We consider a general Gt/Gt/1 singleserver queue with unlimited waiting space and a timevarying arrival rate, where the the service rate at each time is subject to control. We study the ratematching control, where the the service rate is made proportional to the arrival rate. We show that the mod ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
We consider a general Gt/Gt/1 singleserver queue with unlimited waiting space and a timevarying arrival rate, where the the service rate at each time is subject to control. We study the ratematching control, where the the service rate is made proportional to the arrival rate. We show that the model with the ratematching control can be regarded as a deterministic time transformation of a stationary G/G/1 model, so that the queue length distribution is stabilized as time evolves. However, the timevarying virtual waiting time is not stabilized. We show that the timevarying expected virtual waiting time with the ratematching servicerate control becomes inversely proportional to the arrival rate in a heavytraffic limit. We also show that no control that stabilizes the queue length asymptotically in heavytraffic can also stabilize the virtual waiting time. Then we consider two squareroot servicerate controls. We show that these alternative squareroot servicerate controls stabilize the waiting time when the arrival rate changes very slowly relative to the average service time, so that a pointwise stationary approximation is appropriate.
Outage Probabilities in CDMA Networks with Poisson Traffic
 Proc. IEEE Globecom
, 1998
"... In the present paper, we consider a very general model of mobility, and investigate the spatial distribution of active mobile calls in the system at an arbitrary time t. We show that the set of active mobile locations forms a Poisson process in space. We consider a CDMA model with shadowing and dis ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
In the present paper, we consider a very general model of mobility, and investigate the spatial distribution of active mobile calls in the system at an arbitrary time t. We show that the set of active mobile locations forms a Poisson process in space. We consider a CDMA model with shadowing and distancedependent path loss, and with soft handoff. We show that the set of active users in each cell (at time t) forms independent Poisson process in space. We use Campbell's Theorem to characterize the first two moments of the interference of othercell users at each cellsite, and in this way obtain a Gaussian approximation for the othercell interference at time t. We consider an example and use this approximation to calculate outage probabilities and compare with simulation. Our work combines the theory of Poisson processes reviewed in [3], with that of CDMA traffic modeling (see [5]). Due to the length limitation of the present paper, we do not have the opportunity here to develop the notation and theorems of Poisson
Cellular Networks: Transient State Models
, 2000
"... In the article, a part of a cellular mobile communication system is modelled by a queueing network of G=G=N=N stations representing each cell; the network has hexagonal structure, i.e. each G=G=N=N station is connected with six other stations. A method of diffusion approximation is used to study tra ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
In the article, a part of a cellular mobile communication system is modelled by a queueing network of G=G=N=N stations representing each cell; the network has hexagonal structure, i.e. each G=G=N=N station is connected with six other stations. A method of diffusion approximation is used to study transient state probabilities in this model and to investigate timedependent performances of the network. Diffusion approximation allows us to consider a large number of cells, any possible cell capacity and, unlike simulation, to obtain results even in cases where loss probabilities are very small. 1 INTRODUCTION A cellular mobile communication system is usually modelled by a network of multichannel stations, each station corresponding to a cell and the number of channels corresponding to the maximal number of connections served by the cell. Traditional modelling techniques as Markov chain approach and simulation suffer here from their usual drawbacks: state number explosion for Markovian mo...
Stochastic Traffic and Connectivity Dynamics for Vehicular AdHoc Networks in Signalized Road Systems
"... Abstract – In the design and planning of vehicular adhoc networks, roadside infrastructure nodes are commonly used to improve the overall connectivity and communication capability of the networks, however, to determine the locations to install the infrastructure nodes for optimal performance based ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract – In the design and planning of vehicular adhoc networks, roadside infrastructure nodes are commonly used to improve the overall connectivity and communication capability of the networks, however, to determine the locations to install the infrastructure nodes for optimal performance based on the everchanging density and connectivity dynamics of moving vehicles remains to be a challenging issue. In this paper, we introduce a stochastic traffic model to capture the space and time dynamics of vehicles in signalized urban road systems to identify poorlyconnected regions for infrastructure node placements. To closely approximate the practical road conditions, we propose a densitydependent velocity profile to approximate vehicle interactions and capture platoons formation and dissipation at traffic signals. Numerical results are presented to evaluate the stochastic traffic model. In general, we show that the fluid model can adequately describe the mean behavior of the traffic stream, while the stochastic model can approximate the probability distribution well even when vehicles interact with each other as their movement is controlled by traffic lights. With the understandings of the vehicular density dynamics from the proposed model, we illustrate that connectivity dynamics of vehicles can be determined accordingly and consequent system engineering and planning issues such as the identification of poorlyconnected regions in the network for roadside infrastructure node placements can be carried out. I.
REALTIME DELAY ESTIMATION BASED ON DELAY HISTORY IN MANYSERVER SERVICE SYSTEMS WITH TIMEVARYING ARRIVALS
, 2009
"... Motivated by interest in making delay announcements in service systems, we study realtime delay estimators in manyserver service systems, both with and without customer abandonment. Our main contribution here is to consider the realistic feature of timevarying arrival rates. We focus especially o ..."
Abstract
 Add to MetaCart
Motivated by interest in making delay announcements in service systems, we study realtime delay estimators in manyserver service systems, both with and without customer abandonment. Our main contribution here is to consider the realistic feature of timevarying arrival rates. We focus especially on delay estimators exploiting recent customer delay history. We show that timevarying arrival rates can introduce significant estimation bias in delayhistorybased delay estimators when the system experiences alternating periods of overload and underload. We then introduce refined delayhistory estimators that effectively cope with timevarying arrival rates together with nonexponential servicetime and abandonmenttime distributions, which are often observed in practice. We use computer simulation to verify that our proposed estimators outperform several natural alternatives.