1,544 research outputs found
Transient handover blocking probabilities in road covering cellular mobile networks
This paper investigates handover and fresh call blocking probabilities for subscribers moving along a road in a traffic jam passing through consecutive cells of a wireless network. It is observed and theoretically motivated that the handover blocking probabilities show a sharp peak in the initial part of a traffic jam roughly at the moment when the traffic jam starts covering a new cell. The theoretical motivation relates handover blocking probabilities to blocking probabilities in the M/D/C/C queue with time-varying arrival rates. We provide a numerically efficient recursion for these blocking probabilities. \u
Recommended from our members
Finite Time Non-Ruin Probability Formulae for Erlang Claim Interarrivals and Continuous Interdependent Claim Severities
A closed form expression, in terms of some functions which we call exponential Appell polynomials, for the probability of non-ruin of an insurance company, in a finite-time interval is derived, assuming independent, non-identically Erlang distributed claim inter-arrival times, Ļi ā¼ Erlang (gi, Ī»i) , i = 1, 2, . . ., any continuous joint distribution of the claim amounts and any non-negative, non-decreasing real function, representing its premium income. In the special case when Ļi ā¼ Erlang (gi, Ī») , i = 1, 2, . . . it is shown that our main result yields a formula for the probability of non-ruin expressed in terms of the classical Appell polynomials. We give another special case of our non-ruin probability formula for Ļi ā¼ Erlang (1, Ī»i) , i = 1, 2, . . ., i.e., when the inter-arrival times are non-identically exponentially distributed and also show that it coincides with the formula for Poisson claim arrivals, given in [18], when Ļi ā¼ Erlang(1, Ī»), i = 1, 2, . . .. The main result is extended further to a risk model in which inter-arrival times are dependent random variables, obtained by randomizing the Erlang shape or/and rate parameters. We give also some useful auxiliary results which characterize and express explicitly (and recurrently) the exponential Appell polynomials which appear in our finite time non-ruin probability formulae
Fluid Approximation of a Call Center Model with Redials and Reconnects
In many call centers, callers may call multiple times. Some of the calls are
re-attempts after abandonments (redials), and some are re-attempts after
connected calls (reconnects). The combination of redials and reconnects has not
been considered when making staffing decisions, while ignoring them will
inevitably lead to under- or overestimation of call volumes, which results in
improper and hence costly staffing decisions. Motivated by this, in this paper
we study call centers where customers can abandon, and abandoned customers may
redial, and when a customer finishes his conversation with an agent, he may
reconnect. We use a fluid model to derive first order approximations for the
number of customers in the redial and reconnect orbits in the heavy traffic. We
show that the fluid limit of such a model is the unique solution to a system of
three differential equations. Furthermore, we use the fluid limit to calculate
the expected total arrival rate, which is then given as an input to the Erlang
A model for the purpose of calculating service levels and abandonment rates.
The performance of such a procedure is validated in the case of single
intervals as well as multiple intervals with changing parameters
Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective
A call center is a service network in which agents provide telephone-based services. Customers that seek these services are delayed in tele-queues. This paper summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history of a small banking call center, call by call, over a full year. Taking the perspective of queueing theory, we decompose the service process into three fundamental components: arrivals, customer abandonment behavior and service durations. Each component involves different basic mathematical structures and requires a different style of statistical analysis. Some of the key empirical results are sketched, along with descriptions of the varied techniques required. Several statistical techniques are developed for analysis of the basic components. One of these is a test that a point process is a Poisson process. Another involves estimation of the mean function in a nonparametric regression with lognormal errors. A new graphical technique is introduced for nonparametric hazard rate estimation with censored data. Models are developed and implemented for forecasting of Poisson arrival rates. We then survey how the characteristics deduced from the statistical analyses form the building blocks for theoretically interesting and practically useful mathematical models for call center operations. Key Words: call centers, queueing theory, lognormal distribution, inhomogeneous Poisson process, censored data, human patience, prediction of Poisson rates, Khintchine-Pollaczek formula, service times, arrival rate, abandonment rate, multiserver queues.
Some aspects of queueing and storage processes : a thesis in partial fulfilment of the requirements for the degree of Master of Science in Statistics at Massey University
In this study the nature of systems consisting of a single queue are first considered. Attention is then drawn to an analogy between such systems and storage systems.
A development of the single queue viz queues with feedback is considered after first considering feedback processes in general. The behaviour of queues, some with feedback loops, combined into networks is then considered. Finally, the application of such networks to the analysis of interconnected reservoir systems is considered and the conclusion drawn that such analytic methods complement the more recently developed mathematical programming methods by providing analytic solutions for
sub systems behaviour and thus guiding the development of a system model
Stability Analysis of GI/G/c/K Retrial Queue with Constant Retrial Rate
We consider a GI/G/c/K-type retrial queueing system with constant retrial
rate. The system consists of a primary queue and an orbit queue. The primary
queue has identical servers and can accommodate the maximal number of
jobs. If a newly arriving job finds the full primary queue, it joins the orbit.
The original primary jobs arrive to the system according to a renewal process.
The jobs have general i.i.d. service times. A job in front of the orbit queue
retries to enter the primary queue after an exponentially distributed time
independent of the orbit queue length. Telephone exchange systems, Medium
Access Protocols and short TCP transfers are just some applications of the
proposed queueing system. For this system we establish minimal sufficient
stability conditions. Our model is very general. In addition, to the known
particular cases (e.g., M/G/1/1 or M/M/c/c systems), the proposed model covers
as particular cases the deterministic service model and the Erlang model with
constant retrial rate. The latter particular cases have not been considered in
the past. The obtained stability conditions have clear probabilistic
interpretation
Martingale proofs of many-server heavy-traffic limits for Markovian queues
This is an expository review paper illustrating the ``martingale method'' for
proving many-server heavy-traffic stochastic-process limits for queueing
models, supporting diffusion-process approximations. Careful treatment is given
to an elementary model -- the classical infinite-server model , but
models with finitely many servers and customer abandonment are also treated.
The Markovian stochastic process representing the number of customers in the
system is constructed in terms of rate-1 Poisson processes in two ways: (i)
through random time changes and (ii) through random thinnings. Associated
martingale representations are obtained for these constructions by applying,
respectively: (i) optional stopping theorems where the random time changes are
the stopping times and (ii) the integration theorem associated with random
thinning of a counting process. Convergence to the diffusion process limit for
the appropriate sequence of scaled queueing processes is obtained by applying
the continuous mapping theorem. A key FCLT and a key FWLLN in this framework
are established both with and without applying martingales.Comment: Published in at http://dx.doi.org/10.1214/06-PS091 the Probability
Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical
Statistics (http://www.imstat.org
- ā¦