4,379 research outputs found
Busy period analysis of the level dependent PH/PH/1/K queue
In this paper, we study the transient behavior of a level dependent single server queuing system with a waiting room of finite size during the busy period. The focus is on the level dependent PH/PH/1/K queue. We derive in closed form the joint transform of the length of the busy period, the number of customers served during the busy period, and the number of losses during the busy period. We differentiate between two types of losses: the overflow losses that are due to a full queue and the losses due to an admission controller. For the M/PH/1/K, M/PH/1/K under a threshold policy, and PH/M/1/K queues, we determine simple expressions for their joint transforms
Queues and risk processes with dependencies
We study the generalization of the G/G/1 queue obtained by relaxing the
assumption of independence between inter-arrival times and service
requirements. The analysis is carried out for the class of multivariate matrix
exponential distributions introduced in [12]. In this setting, we obtain the
steady state waiting time distribution and we show that the classical relation
between the steady state waiting time and the workload distributions re- mains
valid when the independence assumption is relaxed. We also prove duality
results with the ruin functions in an ordinary and a delayed ruin process.
These extend several known dualities between queueing and risk models in the
independent case. Finally we show that there exist stochastic order relations
between the waiting times under various instances of correlation
Bayesian control of the number of servers in a GI/M/c queuing system
In this paper we consider the problem of designing a GI/M/c queueing system. Given arrival and service data, our objective is to choose the optimal number of servers so as to minimize an expected cost function which depends on quantities, such as the number of customers in the queue. A semiparametric approach based on Erlang mixture distributions is used to model the general interarrival time distribution. Given the sample data, Bayesian Markov chain Monte Carlo methods are used to estimate the system parameters and the predictive distributions of the usual performance measures. We can then use these estimates to minimize the steady-state expected total cost rate as a function of the control parameter c. We provide a numerical example based on real data obtained from a bank in Madrid
Optimizing flow rates in a queueing network with side constraints
Network Analysis;operations research
Backpressure-based control protocols: design and computational aspects
Congestion control in packet-based networks is often realized by feedback protocols. In this paper we assess their performance under a back-pressure mechanism that has been proposed and standardized for Ethernet metropolitan networks. In such a mechanism the service rate of an upstream queue is reduced when the downstream queue is congested, in order to protect the downstream queue. We study a Markovian model that captures the essentials of the protocol, but at the same time allows for numerical analysis. We first derive explicit results for the stability condition of the model (which turns out to be nontrivial). Then we present logarithmic estimates of the probability of buffer overflow in the second queue, which are subsequentially used when devising an efficient simulation procedure based on importance sampling. We conclude the paper by presenting a number of numerical results, and some general design guidelines
BAYESIAN CONTROL OF THE NUMBER OF SERVERS IN A GI/M/C QUEUING SYSTEM
In this paper we consider the problem of designing a GI/M/c queueing system. Given arrival and service data, our objective is to choose the optimal number of servers so as to minimize an expected cost function which depends on quantities, such as the number of customers in the queue. A semiparametric approach based on Erlang mixture distributions is used to model the general interarrival time distribution. Given the sample data, Bayesian Markov chain Monte Carlo methods are used to estimate the system parameters and the predictive distributions of the usual performance measures. We can then use these estimates to minimize the steady-state expected total cost rate as a function of the control parameter c. We provide a numerical example based on real data obtained from a bank in Madrid.
Modeling Supply Networks and Business Cycles as Unstable Transport Phenomena
Physical concepts developed to describe instabilities in traffic flows can be
generalized in a way that allows one to understand the well-known instability
of supply chains (the so-called ``bullwhip effect''). That is, small variations
in the consumption rate can cause large variations in the production rate of
companies generating the requested product. Interestingly, the resulting
oscillations have characteristic frequencies which are considerably lower than
the variations in the consumption rate. This suggests that instabilities of
supply chains may be the reason for the existence of business cycles. At the
same time, we establish some link to queuing theory and between micro- and
macroeconomics.Comment: For related work see http://www.helbing.or
Generalized gap acceptance models for unsignalized intersections
This paper contributes to the modeling and analysis of unsignalized
intersections. In classical gap acceptance models vehicles on the minor road
accept any gap greater than the CRITICAL gap, and reject gaps below this
threshold, where the gap is the time between two subsequent vehicles on the
major road. The main contribution of this paper is to develop a series of
generalizations of existing models, thus increasing the model's practical
applicability significantly. First, we incorporate {driver impatience behavior}
while allowing for a realistic merging behavior; we do so by distinguishing
between the critical gap and the merging time, thus allowing MULTIPLE vehicles
to use a sufficiently large gap. Incorporating this feature is particularly
challenging in models with driver impatience. Secondly, we allow for multiple
classes of gap acceptance behavior, enabling us to distinguish between
different driver types and/or different vehicle types. Thirdly, we use the
novel M/SM2/1 queueing model, which has batch arrivals, dependent service
times, and a different service-time distribution for vehicles arriving in an
empty queue on the minor road (where `service time' refers to the time required
to find a sufficiently large gap). This setup facilitates the analysis of the
service-time distribution of an arbitrary vehicle on the minor road and of the
queue length on the minor road. In particular, we can compute the MEAN service
time, thus enabling the evaluation of the capacity for the minor road vehicles
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