  The Barab\'asi's priority queuing model [A.-L. Barab\'asi, Nature
\textbf{435}, 207 (2005)] and its variants have been extensively studied to
understand heavy-tailed distributions of the inter-event times and the response
times observed in various empirical analyses of human dynamics. In this paper,
we focus on the effects of deadlines assigned to the tasks in a queue of fixed
size on the response-time distributions. Here, the response time is defined as
the time interval between the arrival and the execution of the task. We propose
a deadline-concerning priority queuing model, in which as the deadline
approaches, the priority is adjusted using the inverse of the remaining time to
the deadline. By performing the numerical simulations, we find that the
power-law exponent characterizing the response-time distributions is less than
$1$ under the deterministic selection protocol while it has the value of $1$
under the nondeterministic selection protocol.
