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1.
The intuition while observing the economy of queueing systems, is that one’s motivation to join the system, decreases with
its level of congestion. Here we present a queueing model where sometimes the opposite is the case. The point of departure
is the standard first-come first-served single server queue with Poisson arrivals. Customers commence service immediately
if upon their arrival the server is idle. Otherwise, they are informed if the queue is empty or not. Then, they have to decide
whether to join or not. We assume that the customers are homogeneous and when they consider whether to join or not, they assess
their queueing costs against their reward due to service completion. As the whereabouts of customers interact, we look for
the (possibly mixed) join/do not join Nash equilibrium strategy, a strategy that if adopted by all, then under the resulting
steady-state conditions, no one has any incentive not to follow it oneself. We show that when the queue is empty then depending
on the service distribution, both ‘avoid the crowd’ (ATC) and ‘follow the crowd’ (FTC) scenarios (as well as none-of-the-above)
are possible. When the queue is not empty, the situation is always that of ATC. Also, we show that under Nash equilibrium
it is possible (depending on the service distribution) that the joining probability when the queue is empty is smaller than
it is when the queue is not empty.
This research was supported by The Israel Science Foundation Grant No. 237/02. 相似文献
2.
It has been shown by (R.O. Al-Seedy, A.A. El-Sherbiny, S.A. El-Shehawy, S.I. Ammar, Transient solution of the M/M/c queue with balking and reneging, Comput. Math. Appl. 57 (2009) 1280–1285) that a generating function technique can be successfully applied to derive the transient solution for an M/M/c queueing system. In this paper, we further illustrate how this technique can be used to obtain the busy period density function of an M/M/1 queue with balking and reneging. Finally, numerical calculations are presented. 相似文献
3.
Olga Boudali Antonis Economou 《European Journal of Operational Research》2012,218(3):708-715
We consider a Markovian queue subject to Poisson generated catastrophes. Whenever a catastrophe occurs, all customers are forced to abandon the system, the server is rendered inoperative and an exponential repair time is set on. We assume that the arriving customers decide whether to join the system or balk, based on a natural reward-cost structure. We study the balking behavior of the customers and derive the corresponding Nash equilibrium and social optimal strategies. 相似文献
4.
We consider an M/PH/1 queue with balking based on the workload. An arriving customer joins the queue and stays until served only if the system
workload is below a fixed level at the time of arrival. The steady state workload distribution in such a system satisfies
an integral equation. We derive a differential equation for Phase type service time distribution and we solve it explicitly,
with Erlang, Hyper-exponential and Exponential distributions as special cases. We illustrate the results with numerical examples. 相似文献
5.
We consider an M/PH/1 queue with workload-dependent balking. An arriving customer joins the queue and stays until served if and only if the system
workload is no more than a fixed level at the time of his arrival. We begin by considering a fluid model where the buffer
content changes at a rate determined by an external stochastic process with finite state space. We derive systems of first-order
linear differential equations for the mean and LST (Laplace-Stieltjes Transform) of the busy period in this model and solve
them explicitly. We obtain the mean and LST of the busy period in the M/PH/1 queue with workload-dependent balking as a special limiting case of this fluid model. We illustrate the results with numerical
examples.
相似文献
6.
《Journal of the Egyptian Mathematical Society》2014,22(1):90-95
Recently, [1] have obtained the transient solution of multi-server queue with balking and reneging. In this paper, a similar technique is used to drive a new elegant explicit solution for a two heterogeneous servers queue with impatient behavior. In addition, steady-state probabilities of the system size are studied and some important performance measures are discussed for the considered system. 相似文献
7.
The equilibrium and socially optimal balking strategies are investigated for unobservable and observable single-server classical retrial queues. There is no waiting space in front of the server. If an arriving customer finds the server idle, he occupies the server immediately and leaves the system after service. Otherwise, if the server is found busy, the customer decides whether or not to enter a retrial pool with infinite capacity and becomes a repeated customer, based on observation of the system and the reward–cost structure imposed on the system. Accordingly, two cases with respect to different levels of information are studied and the corresponding Nash equilibrium and social optimization balking strategies for all customers are derived. Finally, we compare the equilibrium and optimal behavior regarding these two information levels through numerical examples. 相似文献
8.
We consider a single server Markovian queue with setup times. Whenever this system becomes empty, the server is turned off.
Whenever a customer arrives to an empty system, the server begins an exponential setup time to start service again. We assume
that arriving customers decide whether to enter the system or balk based on a natural reward-cost structure, which incorporates
their desire for service as well as their unwillingness to wait.
We examine customer behavior under various levels of information regarding the system state. Specifically, before making the
decision, a customer may or may not know the state of the server and/or the number of present customers. We derive equilibrium
strategies for the customers under the various levels of information and analyze the stationary behavior of the system under
these strategies. We also illustrate further effects of the information level on the equilibrium behavior via numerical experiments.
相似文献
9.
M. Jain 《Applied mathematics and computation》2011,217(24):9916-9932
This paper presents modeling and analysis of unreliable Markovian multiserver finite-buffer queue with discouragement and synchronous working vacation policy. According to this policy, c servers keep serving the customers until the number of idle servers reaches the threshold level d; then d idle servers take vacation altogether. Out of these d vacationing servers, dW servers may opt for working vacation i.e. they serve the secondary customers with different rates during the vacation period. On the other hand, the remaining d − dW = dV servers continue to be on vacation. During the vacation of d servers, the other e = c − d servers must be present in the system even if they are idle. On returning from vacation, if the queue size does not exceed e, then these d servers take another vacation together; otherwise start serving the customers. The servers may undergo breakdown simultaneously both in regular busy period and working vacation period due to the failure of a main control unit. This main unit is then repaired by the repairman in at most two phases. We obtain the stationary performance measures such as expected queue length, average balking and reneging rate, throughput, etc. The steady state and transient behaviours of the arriving customers and the servers are examined by using matrix analytical method and numerical approach based on Runge-Kutta method of fourth order, respectively. The sensitivity analysis is facilitated for the transient model to demonstrate the validity of the analytical results and to examine the effect of different parameters on various performance indices. 相似文献
10.
Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs 总被引:1,自引:0,他引:1
We consider the Markovian single-server queue that alternates between on and off periods. Upon arriving, the customers observe the queue length and decide whether to join or balk. We derive equilibrium threshold balking strategies in two cases, according to the information for the server’s state. 相似文献