Tollbooth tandem queues with infinite homogeneous servers

نویسندگان

  • Xiuli Chao
  • Qi-Ming He
  • Sheldon M. Ross
چکیده

In this paper we analyze a tollbooth tandem queueing problem with an infinite number of servers. A customer starts service immediately upon arrival but cannot leave the system before all customers who arrived before himlher have left, i.e. customers depart the system in the same order as they arrive. Distributions of the total number of customers in the system, the number of departure-delayed customers in the system, and the number of customers in service at time t are obtained in closed form. Distributions of the sojourn times and departure delays of customers are also obtained explicitly. Both transient and steady state solutions are derived first for Poisson arrivals, and then extended to cases with batch Poisson and non stationary Poisson arrival processes. Finally, we report several stochastic ordering results on how system performance measures are affected by arrival and service processes.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A tollbooth tandem queue with heterogeneous servers

We study a tandem queueing system with K servers and no waiting space in between. A customer needs service from one server but can leave the system only if all down-stream servers are unoccupied. Such a system is often observed in toll collection during rush hours in transportation networks, and we call it a tollbooth tandem queue. We apply matrix-analytic methods to study this queueing system,...

متن کامل

Longest Path in Networks of Queues in the Steady-State

Due to the importance of longest path analysis in networks of queues, we develop an analytical method for computing the steady-state distribution function of longest path in acyclic networks of queues. We assume the network consists of a number of queuing systems and each one has either one or infinite servers. The distribution function of service time is assumed to be exponential or Erlang. Fu...

متن کامل

Duality and Equivalencies in Closed Tandem Queueing Networks

Equivalence relations between closed tandem queueing networks are established. Four types of models are under consideration: single-server infinite-capacity buffer queues, infinite-server queues with resequencing, single-server unit-capacity buffer queues with blocking before service, and single-server unit-capacity buffer queues with blocking after service. Using a customer/server duality we s...

متن کامل

Object-Oriented Simulation Model for Tandem Tollbooth Operations using Pro-Model

This paper presents a new object-oriented simulation model to describe tandem tollbooth system in order to evaluate the operational performance of toll plaza facilities. This microscopic traffic simulation model is used to enhance planning, design, operations, and management of traffic operation at toll plazas. Computational result shows that lower reaction time ratio increases the throughput c...

متن کامل

A Monotonicity Theorem for Tandem Queues

Tandem queues are often used for performance mod-eling in production lines, computer systems and communication networks. Consider a series of tandem rst-come-rst-served queues with single servers. The buuers may be nite or innnite. When a nite buuer is full, the upstream server may suuer from transfer blocking or service blocking. A job's service requirements at various servers may be correlate...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • J. Applied Probability

دوره 52  شماره 

صفحات  -

تاریخ انتشار 2015