
545 A.2d 619 (1988)
In the Matter of Tilman BORDLEY'S PETITION FOR WRIT OF MANDAMUS.
Supreme Court of Delaware.
Submitted: June 13, 1988.
Decided: July 6, 1988.
Tilman Bordley, Smyrna, pro se.
Richard E. Fairbanks, Jr., Deputy Atty. Gen., Wilmington, for respondent.
Before CHRISTIE, C.J., WALSH and HOLLAND, JJ.
*620 PER CURIAM:
Following a jury trial in the Superior Court, Tilman Bordley, Jr., a/k/a Tilman Wright, Jr. ("Bordley"), was convicted of first degree robbery, second degree conspiracy, possession of a deadly weapon during the commission of a felony, and criminal impersonation. Bordley was sentenced for these convictions on January 6, 1987. On September 14, 1987, Bordley filed a notice of appeal with the Clerk of this Court. This Court dismissed Bordley's direct appeal from his convictions as untimely. Wright v. State, Del.Supr., 535 A.2d 408 (1987).
On February 3, 1988, Bordley filed a motion for postconviction relief, alleging ineffective assistance of counsel. That motion was referred to the trial judge for preliminary consideration pursuant to Superior Court Criminal Rule 61(d). On February 9, 1988, the trial judge, pursuant to Superior Court Criminal Rule 61(g)(2), directed defense counsel to respond to Bordley's allegations within thirty days. Defense counsel responded to Bordley's allegations on April 6, 1988.
This Court now has before it Bordley's pro se petition for a writ of mandamus pursuant to Supreme Court Rule 43. In his petition, Bordley requests this Court to compel the trial judge to take action on his application for postconviction relief. Bordley has alleged that his defense counsel has not responded to the trial judge's order and that this failure constitutes "a substantial disadvantage" to him. The State has filed an answer and a motion to dismiss the petition.
The peremptory writ of mandamus has traditionally been used only to confine a trial court "to a lawful exercise of its prescribed jurisdiction or to compel it to exercise its authority when it is its duty to do so." Roche v. Evaporated Milk Ass'n, 319 U.S. 21, 26, 63 S.Ct. 938, 941, 87 L.Ed. 1185 (1943), quoted in Will v. United States, 389 U.S. 90, 95, 88 S.Ct. 269, 273, 19 L.Ed.2d 305 (1967). See also In re Petition of Justice of the Peace Mabel Pitt, Del.Supr., 541 A.2d 554, 556 (1988). This Court may issue a writ of mandamus when the petitioner can show that he has a clear right to the performance of a duty by a trial court, that no other adequate remedy is available, and that the trial court has arbitrarily failed or refused to perform its duty. See Schagrin Gas Co. v. Evans, Del.Supr., 418 A.2d 997, 998 (1980) (per curiam). Therefore, in the absence of a clear showing of an arbitrary refusal or failure to act, this Court will not issue a writ of mandamus to compel a trial court to perform a particular judicial function, to decide a matter in a particular way, or to dictate the control of its docket. See id.; Norman v. State, Del.Supr., 177 A.2d 347, 349 (1962) (quoting In re Rice, 155 U.S. 396, 15 S.Ct. 149, 39 L.Ed. 198 (1894)).[1]
The case before us contains no showing of an arbitrary refusal to act by the trial judge. Bordley's motion for postconviction relief was referred to the trial judge who then requested and, contrary to Bordley's assertions, received a reply from defense counsel. The trial judge is currently considering the matter pursuant to Superior Court Criminal Rule 61(d). Thus, *621 Bordley's petition for a writ of mandamus must be dismissed.
NOW, THEREFORE, IT IS HEREBY ORDERED, pursuant to Supreme Court Rule 29(b), that the State's motion to dismiss is GRANTED.
NOTES
[1]  Independent of this Court's authority to issue peremptory writs, the Chief Justice, upon the approval of a majority of the Justices of the Supreme Court, has "general administrative and supervisory powers over all the courts" of this State. Del. Const. art. IV, § 13.
