Autocorrelations in infinite server batch arrival queues

DOI10.1007/BF01158871zbMath0790.60082OpenAlexW2036263880MaRDI QIDQ1319845

J. G. C. Templeton, Li-Ming Liu

Publication date: 20 June 1994

Published in: Queueing Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01158871

zbMATH Keywords

batch arrivalautocorrelationbatch sizesMarkov renewal input processcustomer dependence

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22)

Related Items

INFINITE-SERVER QUEUES WITH BATCH ARRIVALS AND DEPENDENT SERVICE TIMES, Departures in \(GR^{X_ n}/ G_ n/ \infty\), Queue lengths in the \(GI^ X/M^ R/\infty\) service system, Two-parameter heavy-traffic limits for infinite-server queues with dependent service times, Markov-modulated infinite-server queues with general service times, A functional law of the iterated logarithm for multi-class queues with batch arrivals, On the distributions of infinite server queues with batch arrivals

Cites Work

• Unnamed Item
• Unnamed Item
• The \(GR^{X_ n}/G_ n/\infty\) system: System size
• Means and variances of time averages in Markovian environments
• Limit theorems for a \(GI/G/\infty\) queue
• Networks of infinite-server queues with nonstationary Poisson input
• On limit laws for service processes in multi-channel systems
• The correlation functions of rbm and m/m/1
• On the GI^X/G/∞ system
• A new view of the heavy-traffic limit theorem for infinite-server queues
• On a coincidence problem concerning telephone traffic
• Some asymptotic formulas for markov chains with applications to simulation^†
• A diffusion approximation for correlation in queues
• Formulas for the variance of the sample mean in finite state markov processes
• Heavy-Traffic Limits for Queues with Many Exponential Servers
• A note on networks of infinite-server queues
• On the heavy-traffic limit theorem for GI/G/∞ queues
• Linear Estimators for a Class of Stationary Queueing Processes
• Asymptotic Formulas for Markov Processes with Applications to Simulation
• The covariance structure of queues and related processes – a survey of recent work
• The stable M/G/1 queue in heavy traffic and its covariance function
• On infinite server queues with batch arrivals
• An application of stationary point processes to queueing theory and textile research
• Limiting diffusion approximations for the many server queue and the repairman problem
• On linearly regressive processes
• The infinite server queue with semi-Markovian arrivals and negative exponential services